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a)Find the mean and the mode.

b)Display the data using a stem-and-leaf plot.

c)Find the five number summary.

3.The mean score of a competency test is 82, with a standard deviation of 2. (Assume the data set has a bell-shaped distribution). What percent of the scores lie between 80 and 86.

3.A student receives test scores of 72 and 83, a final exam score of 88, and a homework score of 96. Each test is 25%, the final exam is 35%, and the homework is 15% of the final grade. What is the weighted mean of his score?

15.A survey indicates that 53% of women in the U.S. consider reading their favorite hobby. You randomly select five U.S. women and ask them if reading is their favorite hobby.

a)Determine the values of n, p, q, x.

b) Find the probability that four of them respond yes.

c)Find the probability that at least four of them respond yes.

d) Find the mean and the standard deviation.

15.Find the area under the standard normal curve

a)to the left of z = - 0.98.

b) to the right of z = 1.06.

c)between z = -1.5 and z = 1.25.

15.Scores for a certain test are normally distributed, with a mean of 50 and a standard deviation of 10. An agency will hire applicants with scores in the top 15%. What is the lowest score in the top 15%?

The lengths of pregnancies are normally distributed with a mean of 268 days and a standard deviation of 15 days.

a)Find the probability that the length of pregnancy is more than 264 days.

b)Out of 200 pregnancies, how many would be more than 264 days?

c)If 36 women are randomly selected, find the probability that they have a mean pregnancy between 264 days and 266 days.

24.A random sample of 40 students has a test score with mean 81.5. Assume the population standard deviation is 10.2. Construct the 90% confidence interval for the population mean.

24.The standard IQ test has a mean of 96 and a standard deviation of 14. We want to be 95% certain that we are within 4 points of the true mean. Find the sample size.

24.Construct a 95% confidence interval for the population mean, . Assume the population has a normal distribution. A sample of 25 randomly selected students has a mean test score of 81.5 with a standard deviation of 10.2.

33.One of your distributors reports that the average sale is 150 per day. You randomly select 35 days and determine the number of sales each day. The sample mean is 143 sales with a standard deviation of 15 sales. You want to test the distributor's claim at = 0.01.

a)State the hypotheses, and identify the claim.

b)Determine whether the test is left-tailed, right-tailed, or two-tailed.

c)Find the standardized test statistic z.

d)Find the P-value.

e)Decide whether to reject the null hypothesis or not.

f)Interpret the decision in the context of the claim.