A credit card company claims that the mean credit card debt for individuals is greater than $5,300. You want to test this claim. You find that a random sample of 36 cardholders has a mean credit card balance of $5,491 and a standard deviation of $50. At a= 0.01, can you support the claim? Complete parts (a) through (e) below. Assume the population is normally distributed. (a) Write the claim mathematically and identify Hg and H, Which of the following correctly states Họ and H,? O A. Họ: u> $5,300 H, us $5,300 O B. Ho: us $5,300 H, p> $5.300 OC. Họ > $5,300 H, us$5,300 OF. Ho: = $5,300 OD. Ho: Ha $5,300 H,p< $5.300 O E. Ho: $5,300 H, p> $5.300 H, urS5.300 (b) Find the critical value(s) and identify the rejection region(s). What is(are) the critical value(s). to? to = 0 (Use a comma to separate answers as needed. Round to three decimal places as needed.) Determine the rejection region(s). Select the correct choice below and fill in the answer box(es) within your choice. (Round to three decimal places as needed.) OA. t O B. t and t> OD. et (c) Find the standardized test statistic t. t= (Round to two decimal places as needed.) (d) Decide whether to reject or fail to reject the null hypothesis. O A. Fail to reject Hg because the test statistic is not in the rejection region. O B. Reject H, because the test statistic is not in the rejection region. OC. Fail to reject H, because the test statistic is in the rejection region. O D. Reject Ho because the test statistic is in the rejection region.

Assume that adults have IQ scores that are normally distributed with a mean of 102.1 and a standard deviation 16.3. Find the first quartile Q1​, which is the IQ score separating the bottom​ 25% from the top​ 75%. (Hint: Draw a​ graph.)

Find the indicated IQ score. The graph to the right depicts IQ scores of​ adults, and those scores are normally distributed with a mean of 100 and a standard deviation of 15.

According to a recent survey, the salaries of entry-level positions at a large company have a mean of $40,756 and a standard deviation of $6500. Assuming that the salaries of these entry-level positions are normally distributed, find the proportion of employees in entry-level positions at the company who earn at least $53,000. Round your answer to at least four decimal places. X Ś

A standardized exam's scores are normally distributed. In a recent year, the mean test score was 1539 and the standard deviation was 315. The test scores of four students selected at random are 1940, 1290, 2240, and 1420. Find the z-scores that correspond to each value and determine whether any of the values are unusual. The z-score for 1940 is. (Round to two decimal places as needed.) The Z-score for 1290 is. (Round to two decimal places as needed.) The Z-score for 2240 is. (Round to two decimal places as needed.) The Z-score for 1420 is. (Round to two decimal places as needed.) Which values, if any, are unusual? Select the correct choice below and, if necessary, fill in the answer box within your choice. OA. The unusual value(s) is/are. CD (Use a comma to separate answers as needed.) OB. None of the values are unusual.

Pay your bills: In a large sample of customer accounts, a utility company determined that the average number of days between when a bill was sent out and when the payment was made is 29 with a standard deviation of 5 days. Assume the data to be approximately bell-shaped. Answer the question below.

Assume that adults have IQ scores that are normally distributed with a mean of 97.8 and a standard deviation 22.5. Find the first quartile ​Q1, which is the IQ score separating the bottom​ 25% from the top​ 75%. (Hint: Draw a​ graph.)

Find the indicated IQ score. The graph to the right depicts IQ scores of adults, and those scores are normally distributed with a mean of 100 and a standard deviation of 15.

The Internal Revenue Service reports that the mean federal income tax paid in the year 2010 was $8040. Assume that the standard deviation is $4900. The IRS plans to draw a sample of 1000 tax returns to study the effect of a new tax law. Do you think it would be unusual for an individual to pay a tax of less than $7800? Explain. Assume the variable is normally distributed. Round the answer to at least four decimal places.