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business statistics using excel

Questions and Answers of Business Statistics Using Excel

Assume you have a fair coin and wish to know the probability that you would get eight heads out of ten flips. The binomial distribution has a mean of μ = np = 10 * 0.5 = 5 and a variance of σ2 =
A quality control system selects a sample of three items from a production line. If one or more is defective, a second sample is taken (also of size three), and if one or more of these are defective
Enquiries at a travel agent lead to a holiday booking being made only sometimes. The agent needs to make 35 bookings per week to break even. If during a week there are 100 enquiries and the
Five people in seven voted in an election. If four of those on the roll are interviewed what is the probability that at least three voted?
A small tourist resort has a weekend traffi c problem and is considering whether or not to provide emergency services to help mitigate the congestion that results from an accident or breakdown. Past
The average number of broken eggs per lorry is known to be 50. What is the probability that there will be more than 70 broken eggs on a particular lorry load?We may use the normal approximation to
Calculate P(0), P(1), P(2), P(3), P(4), P(5), P(6), and P(>6) for a Poisson variable with a mean of 1.2. Using this probability distribution determine the mean and variance.
In a machine shop the average number of machines out of operation is two. Assuming a Poisson distribution for machines out of operation, calculate the probability that at any one time there will
A factory estimates that 0.25% of its production of small components is defective. These are sold in packets of 200. Calculate the percentage of the packets containing one or more defectives.
The average number of faults in a metre of cloth produced by a particular machine is 0.1. (a) What is the probability that a length of four metres is free from faults? (b) How long would a piece
A garage has three cars available for daily hire. Calculate the following probabilities if the variable is a Poisson variable with a mean of 2: (a) Find the probability that on a given day that
Accidents occur in a factory randomly and, on average, at the rate of 2.6 per month. What is the probability that in a given month: (a) No accidents will occur (b) More than one accident will occur?
A new telephone directory is to be published. Before publication entries are proofread for errors and any corrections made. Experience suggests that, on average, 0.1% of the entries require
Given X is a discrete binomial random variable with p = 0.3 and n = 20: (a) Can we use the normal approximation to estimate the binomial probability? (b) What if n is changed to 15? (c) if n = 40
Concerned at the time to react to customer complaints CoCo S.A. has implemented a new set of procedures for its support centre staff. The customer service director has directed that a suitable test
A local maternity hospital has an average of 36 births per week. Use this information to calculate the following probabilities: (a) The probability that there are fewer than 30 births in a given
Five people have all made claims for the amounts shown in Table 5.2A sample of two people is to be taken at random, with replacement, from the five. Derive the sampling distribution of the mean and
To illustrate this property consider the problem of tossing a fair die. The die has 6 numbers (1, 2, 3, 4, 5, and 6), with each number likely to have the same frequency of occurrence. If we then take
Bakers Ltd is currently undertaking a review of the delivery vans used to deliver products to customers. The company runs two types of delivery van (type A, recently purchased, and type B, at least 3
Diet X runs a number of weight reduction centres within a large town in the north east of England. From the historical data it was found that the weight of participants is normally distributed with a
Skodel Ltd is developing a low calorie lager for the European market with a mean designed calorie count of 43 calories per 100 ml. The new product development team are having problems with the
If X is a normal random variable with mean 10 and standard deviation 2, i.e. X ~ N (10, 4). Define and compare the sampling distribution for samples of size: (a) 2, (b) 4,(c) 16.
Calculate the probability that the sample mean lies between 146 and 158 pounds.
If X is any random variable with mean = 63 and standard deviation = 10. Define and compare the sampling distribution for samples of size:(a) 40, (b) 60, (c) 100.
A random sample of 30 part-time employees is chosen without replacement from a firm employing 200 part-time workers. If the mean hours worked per month is 60 hours with a standard deviation of 5
Consider the sampling of 50 electrical components from a production run where, historically, the component’s average lifetime was found to be 950 hours with a standard deviation of 25 hours. The
Assuming that the weights of 10,000 items are normally distributed and that the distribution has a mean of 115 kg and a standard deviation of 3 kg: (a) Estimate how many items have weights between
It is known that 25% of workers in a factory own a personal computer. Find the probability that at least 26% of a random sample of 80 workers will own a personal computer. In this example, we have
By treating the following as finite and infinite samples comment on the standard errors: (a) Find the sample mean and standard error for random samples of 1000 accounts if bank A has 5024 saving
Consider the problem of sampling from a population which consists of the salaries for public sector employees employed by a national government. The historical data suggests that the population data
A sample of 100 was taken from a population with π = 0.5. Find the probability that the sample proportion will lie between: (a) 0.4 and 0.6, (b) 0.35 and 0.65, (c) 0.5 and 0.65.
An experiment on the measurement of the length of rods was performed five times, with the following results: 1.010, 1.012, 1.008, 1.013, and 1.011. Calculate the unbiased estimates of the mean and
From a parliamentary constituency a sample of 100 people were asked whether they would vote Labour or Conservative. It is thought that 40% of the constituency will favour Labour. Find the approximate
In a sample of 400 textile workers, 184 expressed dissatisfaction regarding a prospective plan to modify working conditions. Provide a point estimate of the population proportion of total workers who
The annual income of doctors constitutes a highly positive-skewed distribution. Suppose the population has an unknown mean and a standard deviation of £10,000. An estimate of the population mean is
Eight samples measuring the length of cloth are sampled from a population where the length is normally distributed with population standard deviation 0.2. Calculate a 95% confidence interval for the
The average number of Xerox copies made in a working day in a certain office is 356 with a standard deviation of 55. It costs the firm three pence per copy. During a working period of 121 days what
A researcher determines that a margin of error (or sampling error, e) of no more than ± 0.5 units is desired, along with a 98% confidence interval. If we assume a normal population standard
A random sample of 5 values was taken from a population: 8.1, 6.5, 4.9, 7.3, and 5.9. Estimate the population mean and standard deviation, and the standard error of the estimate for the population
The mean of 10 readings of a variable was 8.7 with standard deviation 0.3. A further 5 readings were taken: 8.6, 8.5, 8.8, 8.7, and 8.9. Estimate the mean and standard deviation of the set of
Two samples are drawn from the same population as follows: sample 1 (0.4, 0.2, 0.2, 0.4, 0.3, and 0.3) and sample 2 (0.2, 0.2, 0.1, 0.4, 0.2, 0.3, and 0.1). Determine the best unbiased estimates of
A random sample of 100 rods from a population line were measured and found to have a mean length of 12.132 with standard deviation 0.11. A further sample of 50 is taken. Find the probability that the
A random sample of 20 children in a large school were asked a question and 12 answered correctly. Estimate the proportion of children in the school who answered correctly and the standard error of
A random sample of 500 fish is taken from a lake and marked. After a suitable interval a second sample of 500 is taken and 25 of these are found to be marked. By considering the second sample
The standard deviation for a method of measuring the concentration of nitrate ions in water is known to be 0.05 ppm. If 100 measurements give a mean of 1.13 ppm, calculate the 90% confidence limits
In trying to determine the sphere of influence of a sports centre a random sample of 100 visitors was taken. This indicated a mean travel distance (d) of 10 miles with a standard deviation of 3
The masses, in grams, of 13 ball bearings taken at random from a batch are: 21.4, 23.1, 25.9, 24.7, 23.4, 24.5, 25.0, 22.5, 26.9, 26.4, 25.8, 23.2, and 21.9. Calculate a 95% confidence interval for
Concerned at the time taken to react to customer complaints, CoCo S.A. has implemented a new set of procedures for its support centre staff . The customer service director has directed that a
A business analyst has been requested by the managing director of a national supermarket chain to undertake a business review of the company. One of the key objectives is to assess the level of
The historical output by employees is a mean rate of 100 units per hour with a standard deviation of 20 units per hour. A new employee is tested on 36 separate random occasions and is found to have
Bakers Ltd are currently undertaking a review of the delivery vans used to deliver products to customers. The company runs two types of delivery van (type A, recently purchased, and type B, at least
A supermarket is supplied by a consortium of milk producers. Recently, a quality assurance check suggests that the amount of milk supplied is significantly different from the quantity stated within
Employees of a firm produce units at a rate of 100 per hour with a standard deviation of 20 units per hour. A new employee is tested on 36 separate random occasions and is found to have an output of
Skodel Ltd is developing a low calorie lager for the European market with a mean designed calorie count of 43 calories per 100 ml. The new product development team are having problems with the
A business analyst is attempting to understand visually the meaning of the critical test statistic and the p-value. For a z value of 2.5 and significance level of 5% provide a sketch of the normal
A local car dealer wants to know if the purchasing habits of a buyer buying extras have changed. He is particularly interested in male buyers. Based upon collected data he has estimated that the
What are the critical z values for a significance level of 2%: (i) Two tail, (ii) Lower one tail,(iii) Upper one tail?
A large organization produces electric light bulbs in each of its two factories (A and B). It is suspected that the quality of production from factory A is better than from factory B. To test this
A marketing manager has undertaken a hypothesis test to test for the difference between accessories purchased for two different products. The initial analysis has been performed and an upper one tail
A mobile phone company is concerned at the lifetime of phone batteries supplied by a new supplier. Based upon historical data this type of battery should last for 900 days with a standard deviation
Concerned by the number of passengers not wearing rear seat belts in cars, a local police authority decided to undertake a series of surveys based upon two large cities. The survey consisted of two
A local Indian restaurant advertises home delivery times of 30 minutes. To monitor the eff ectiveness of this promise the restaurant manager monitors the time that the order was received and the time
A certain product of organic beans are packed in tins and sold by two local shops. The local authority have received complaints from customers that the amount of beans within the tins sold by the
Calculate the critical t values for a significance level of 1% and 12 degrees of freedom:(i) Two tail, (ii) Lower one tail, (iii) Upper one tail.
After further data collection the marketing manager (Exercise X6.4) decides to revisit the data analysis and changes the type of test to a t-test. (i) Explain under what conditions a t-test could be
A certain product of organic beans is packed in tins and sold by two local shops. The local authority have received complaints from customers that the amount of beans within the tins sold by the shop
A tyre manufacturer conducts quality assurance checks on the tyres that it manufactures. One of the tests consists of undertaking a test on their medium-quality tyres with an independent random
Suppose that Super Slim is advertising a weight reduction programme that they say will result in more than 10 lb weight loss in the first 30 days. Twenty-six subjects were independently and randomly

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