QUESTION 1

A class has 80 students.Test 2 had a class average of 78 and a variance of 49.Answer the following 7 questions.(Assume Normal distribution).Assume a 90-80-70-60 = A-B-C-D scale.

1.What is the probability of getting an A?

2.How many will get an A?

3.What is the probability of getting a B?

4.What is the probability of getting a C?

5.How many people will fail the class?

6.If the bottom 5% will get an F, what will be the cut-off score?

7.If the top 15% get an A, what is the cutoff score for an A?

QUESTION 2

A visit to a hospital emergency room for something as simple as a sore throat could have amean cost of $328.Assume that this cost is normally distributed with a standard deviation of $82.If you want to be in the bottom 50%, what will be the cut-offdollar amount?

QUESTION 3

A visit to a hospital emergency room for something as simple as a sore throat could have amean cost of $320.Assume that this cost is normally distributed with a standard deviation of $89.What is the cut-off dollar amount if you want to be in the top 3% of the patients?

QUESTION 4

For a standard normal distribution, the probability of obtaining azvalue between -1.9 to 1.7 is ?

QUESTION 5

Pioneer companyhas given an aptitude test to 71 potential job applicants.The test score had an average of81 and a standard deviation of 8.Aptitude tests are known to follow a t-distribution.Pioneer rejects the bottom 5% of the applicants right away.The top 5% are hired immediately at managerial positions.Answer the next 6 questions.

a.What is the degrees of freedom for this distribution?

b.What is the t-score for someone who has scored 93?

c.What is the cutoff score for those who'll be hired as managers?

d.Whatwill be the cutoff score fro those who'll get rejected right away?

e.If we want to define the middle of the class (80%) to be average,what will be the lower cut-off scores?

f.If we want to define the middle of the class (80%) to be average,what will be the upper cut-off scores?

QUESTION 6

Suppose a tire manufacturer wants to set a mileage guarantee on its new XB 70 tire. Tests revealed that the tire's mileage is normally distributed with a mean of 47,900 miles and a standard deviation of 2,050 miles. The manufacturer wants to set the guaranteed mileage so that no more than 5 percent of the tires will have to be replaced. What guaranteed mileage should the manufacturer announce?

44? 52832? 96049? 62140? or 922?

QUESTION 7

Suppose the probability of someone wearing a pair of glasses among 5th graders is 24%.If there are 51 kids in a class, what will be the standard deviation of this distribution?

QUESTION 8

Suppose the probability of someone wearing a pair of glasses among 5th graders is 35%.If there are 54 kids in a class, how many of them are expected to have glasses?

QUESTION 9

The assembly time for a product is uniformly distributed between 6 and 10 minutes.What is the probability that on a given day, the product will take between 7.4 and 8.3 minutes?

QUESTION 10

The average spending at Neco's salad bar is $9.6 with a standard deviation of $3.26.The distribution follows Normal distribution.The management is interested in the middle 85% of the customers (spending wise) as it believes that they represent the customer base.What will be the difference between the upper and lower spending cut-offs which define the middle 85% of the customers?

QUESTION 11

The average spending at Neco's salad bar is $8.08 with a standard deviation of $2.6.The distribution follows t-distribution.The management is interested in the middle 90% of the customers (spending wise) as it believes that they represent their true customer base.What will be the difference between the upper and lower spending cut-offs which define the middle 90% of the customers if the sample contains 41 customers?

QUESTION 12

The average spending at Neco's salad bar is $9.83 with a standard deviation of $3.06.The distribution follows Normal distribution.The management is interested in the middle 80% of the customers (spending wise) as it believes that they represent the customer base.What will be the difference between the upper and lower spending cut-offs which define the middle 80% of the customers?

QUESTION 13

The baking time for a cake isuniformly distributed between 16 and 22 minutes.What is the probability that on a given day, the product will take more than19.1minutes?

QUESTION 14

The weights of the potatoes is your garden is normally distributed.If the middle 95.44% weigh between 5.8 and 9.19 ounces, then what is the standard deviation of the weights?

QUESTION 15

The weights of the tomatoes is normally distributed.If the middle 83% weigh between 2.35 ounces and 5.53 ounces, then what is the mean weight of the tomatos?

QUESTION 16

Zis a standard normal variable. Find the value ofzin the following.

1. The area between 0 andzis 0.4678.
2. The area to the right ofzis 0.1112.
3. The area to the left ofzis 0.8554
4. The area between -zandzis 0.754.
5. The area to the left ofzis 0.0681.
6. The area to the right ofzis 0.9803.

QUESTION 17

There are 90 people in the restaurant.The probability of someone ordering a drink with the food is 60%.Use Normal approximation of Binomial Distribution to answer the following 6 questions.

1. What is the mean of the Normal distribution?

2. What is the standard deviation of the normal distribution?

3. What is the probability that exactly 50 people will order a drink?

4. What the probability that more than 50 people will order a drink?

5. What is the probability that less than 50 people will order a drink?

6. What is the probability that between 52 or more and 56 or less people will order a drink?