The producer of a weight-loss pill advertises that people who use the pill lose, after one week, an average (mean) of 1.85 pounds with a standard deviation of 1.05 pounds. In a recent study, a group of 60 people who used this pill were interviewed. The study revealed that these people lost a mean of 1.88 pounds afte one week. If the producer's claim is correct, what is the probability that the mean weight loss after one week on this pill for a random sample of 60 individuals will be 1.88 pounds or less? Carry your intermediate computations to at least four decimal places. Round your answer to at least three decimal places.

An analyst found that the average amount of money in bank accounts at his/her bank is $2,000 with a standard deviation of $150.  What would be the variance?

A report about how American college students manage their finances includes data from a survey of college students. Each person in a representative sample of 793 college students was asked if they had one or more credit cards and if so, whether they paid their balance in full each month. There were 500 who paid in full each month. For this sample of 500 students, the sample mean credit card balance was reported to be $825. The sample standard deviation of the credit card balances for these 500 students was not reported, but for purposes of this exercise, suppose that it was $205. Is there convincing evidence that college students who pay their credit card balance in full each month have a mean balance that is lower than $907, the value reported for all college students with credit cards? Carry out a hypothesis test using a significance level of 0.01.   State the appropriate null and alternative hypotheses. H0: ? = 907 Ha: ? < 907 H0: ? = 907 Ha: ? > 907      H0: ? < 907…

The Aluminum Association reports that the average American uses 56.8 pounds of aluminum in a year. A random sample of 50 households is monitored for one year to determine aluminum usage. If the population standard deviation of annual usage is 12.3 pounds, what is the probability that the sample mean will be each of the following? Appendix A Statistical Tables d. Less than 55 poundse. Less than 49 pounds

The heights of women in the United States are normally distributed with a mean of 63.7 inches and a standard deviation of 2.7 inches. If you randomly select a woman in the United States, what is the probability that she will be between 65 and 67 inches tall?

A successful basketball player has a height of 6 feet 11 ​inches, or 211 cm. Based on statistics from a data​ set, his height converts to the z score of 5.17. How many standard deviations is his height above the​ mean?

In the class of 2019, more than 1.6 million students took the SAT. The distribution of scores on the math section (out of 800) is approximately normal with a mean of 528 and standard deviation of 117.  What proportion of students earned scores between 500 and 600 on the SAT math test?

A bank's loan officer rates applicants for credit. The ratings are normally distributed with a mean of 200 and a standard deviation of 50. If an applicant is randomly selected, find the probability of a rating that is greater than 295.

Last year, the average amount that teams for the Statistics Games raised was $375. Have teams been more successful at fundraising this year? To find out, you take a random sample of 36 teams. Your sample of 36 teams yields a mean of $396 and a standard deviation of $70. Might you have made a Type 1 or Type 2 error? A Type 1. This means that we said that the mean amount raised had increased, when it was actually still $375. B You might have made a calculation error. C Neither- we're sure the average has increased. D Type 2. This would mean that we said there was not enough evidence to say the mean had increased from $375, when it actually is higher than $375. E Either kind is possible!

A college student is interested in investigating the claim that students who graduate with a master’s degree earn higher salaries, on average, than those who finish with a bachelor’s degree. She surveys, at random, 49 recent graduates who completed their master’s degrees, and finds that their mean salary is $⁢37,400 per year. The standard deviation of annual salaries for the population of recent graduates who have master’s degrees is known to be $⁢2400. She also surveys, at random, 37 recent graduates who completed their bachelor’s degrees, and finds that their mean salary is $⁢36,700 per year. The standard deviation of annual salaries for the population of recent graduates with only bachelor’s degrees is known to be $⁢1900. Test the claim at the 0.05 level of significance. Let recent graduates with a master's degree be Population 1 and let recent graduates with a bachelor's degree be Population 2.   Step 3 of 3 :   Draw a conclusion and interpret the decision.