Solve the question.

A student takes a 20-question, True/False exam and guesses

on each question. Find the probability of passing if the lowest

grade is 15 correct out of 20.

4 A new surgical procedure is said to be successful 80% of times.

Suppose the operation is performed five times, and the results

are assumed to be independent of one another. What are the

probabilities of these events

a All five operators are successful.

b Exactly four are successful.

c Less than two are successful.

d More than 3 are successful

e Find the variance and the standard deviation

5 A study found that 1% of social security recipients are too

young to vote, if 800 social security recipients are randomly

selected. Find the mean, variance, and the standard deviation

of the number of recipients who are too young to vote.

6 If 3% of calculators are defective, find the mean, variance, and

standard deviation of a lot of 300 calculators.

7 Thirty-two percent of adult Internet users have purchased

products or services online. For a random sample of 200 adult

Internet users, find the mean, variance, and standard deviation

for the number who have purchased good, or services online

The owner of a popular barber shop in ?stanbul is anxious about reducing the total time a customer spends (i.e waiting to be served plus time served) in the barber shop. They randomly select six customers each day and find the total time they spent in the shop. Using these 6 observations they find the sample mean and range R. These observations are repeated for 50 days. The summary data for these 50 samples are given as:

Mean of the 50 sample means = 50 and the mean of 50 sample Ranges = 6.

(a)Construct the Mean X- and R- chart upper and lower control limits.

(b)Find the percentage of customers who will not have spent more than 60 minutes in the shop, assuming that time spend in the barber shop is distributed normally.

(c)The owner of the barber shop, reduces the average time spent in shop to 40 minutes by employing more workers. With this new average time what proportion of customers will have to stay in the shop longer than 45 minutes?

\fA new process is applied to a part which should reduce its surface roughness. 5 parts are chosen, and each part's roughness is measured before and after the process is applied, resulting in the data below. Is the new process effective? Perform the appropriate hypothesis test using a significance level of 0.05. State H5, H1, or, your test statistic, the test's critical value, and conclusion (both statistically and in practical terms). Part Surface Roughness Before After DeltaBefDre_After 1 32.3 24.3 8.0 2 31.5 28.6 2.9 3 30.5 25.2 5.4 4 33.4 29.4 4.0 5 32.8 30.1 2.7 Xbar: 32.12 27.52 4.6 S: 1.0986 2.6033 2.1829 Problem 4 (7 points) Trace metals in drinking water affect the flavor and an unusually high concentration can pose a health hazard. 7 pairs of data were taken measuring zinc concentration in bottom water and surface water Zinc concentration in bottom water .27 57 .53 .71 72 .65 .58 Zine concentration in surface water .47 .72 .61 .52 .41 .61 Does the data suggest that the true average concentration in the bottom water exceeds that of surface water? (a) Set up the hypotheses. (b) Compute the test statistic. Check whether to reject the null hypothesis by comparing the test statistic by the tabular one. (c) Calculate the p-value and use it to test the hypothesis. (d) Construct a 95% confidence interval for the difference means in zinc concentration in bottom water and surface water. (e) Use the results in part (d) to test the hypothesis using the significant level 0.05,Two technicians measured the surface finish of a metal part, obtaining the data presented in the table below. Assume that the measurements are normally distributed. The to test statistic was calculated for these measurements resulting in a value of to = 0.11. Using & = 0.05 and assuming equal variances, the following test hypothesis was tested for the mean surface finish measurements made by the two technicians: Ho: HI - H2 = 0, H1:/1 - 12+ 0 Based on the above information, which of the following statement(s) are correct? Technician 1 Technician 2 1.45 1.54 1.37 1.41 1.21 1.56 1.54 1.37 1.48 1.20 1.29 1.31 1.34 1.27 1.35 If the null hypothesis should be rejected, we would be concerned that the technicians obtain different measurements. It does not matter which technician measures parts; the readings will be statistically the same Do not reject the Ho and conclude that there is sufficient statistical evidence of a difference between measurements obtained by the two technicians The degree of freedom of the calculated test statistic is N-1 = 6. The mean surface finish measurements by the two technicians are not statistically equal