Estimating Mean and Standard Deviation

A certain variety of table grapes has fruit diameters that are distributed normally with mean 13 mm and standard deviation 2 mm. If you take a sample of 16 grapes, approximately what value represents the 80th percentile for the sample mean?

• 12.60

• 12.58

• 13.42

• 13.40

The mean July daily rainfall in Hulu Kinta is 10 mm and the standard deviation is 1.5 mm. What is the probability that the average rainfall for the month of July will be less than 9.5 mm? (31 days in July)

• 0.0918

• 0.3707

• 0.9686

• 0.0314

The ages of the population of people living in Meru, Malaysia are normally distributed with a mean of 43 and standard deviation of 14. If you take a sample of 49 people, what it the probability the sample mean will be greater than 46?

• 0.9332

• 0.0668

• 0.5832

• 0.0013

An article investigated whether education programs for nurses improve the outcomes for their older patients. The standard deviation of the lengths of hospital stay on the intervention ward is 8.3 days. What is the probability that the sampling error made in estimating the mean length of stay of a sample of 80 patients will be at most 2 days?

• 0.9692

• 0.9846

• 0.9544

• 0.9772

Mr. Greider wants to curve his Calculus test scores. They currently have an average of 66 with a standard deviation of 5 points. His highest score was an 80, so he decided to double every score and then subtract 60 points. What would be the new expected mean and standard deviation? What problem might this cause for students that scored below a 60?

• The new expected mean is 72 and the standard deviation is 10. Students scoring below 60 will have negative scores.

• The new expected mean is 66 and the standard deviation is 5. Students scoring below 60 will have scores above 60.

• The new expected mean is 132 and the standard deviation is 10. Students scoring below 60 will have scores above 60.

• The new expected mean is 72 and the standard deviation is 5. Students scoring below 60 will have negative scores.

Mike, Steve and Phil are going to compete in a triathlon relay. Mike will do the swimming leg. He can typically do the swim in an average of 23 minutes with a standard deviation of 5 minutes. Steve will do the run. He typically does the run in an average of 55 minutes with a standard deviation of 6 minutes. Phil will do the bike. His average bike time is 46 minutes with a standard deviation of 3 minutes. What should they expect the mean and standard deviation of their combined times to be?

• Mean: 124 minutes, Standard Deviation: 14 minutes

• Mean: 124 minutes, Standard Deviation: 7.81 minutes

• Mean: 124 minutes, Standard Deviation: 8.37 minutes

• Mean: 124 minutes, Standard Deviation: 9.27 minutes

A company wants to sell trail mix. They decide to mix M&M’s with peanuts. Weights of bags of M&M’s have a mean of 7.6 ounces with a standard deviation of 1.3 ounces. Bags of peanuts that will be mixed with the M&M’s have a mean weight of 6.5 ounces with a standard deviation of 0.9 ounces. When the bags are mixed what is the expected combined mean and standard deviation?

• Mean: 14.1 ounces, Standard Deviation: 1.6 ounces

• Mean: 14.1 ounces, Standard Deviation: 2.2 ounces

• Mean: 14.1 ounces, Standard Deviation: 1.1 ounces

• Mean: 14.1 ounces, Standard Deviation: 2.0 ounces

A fleet of cars from Ford has an average MPG of 24 with a standard deviation of 4 mpg. Ford installs a new chip in the computers that will increase the gas mileage by 20%. What will the mean and standard deviation of the new MPG’s be?

• Mean: 28.8 MPG, Standard Deviation: 4.8 MPG

• Mean: 28.8 MPG, Standard Deviation: 4 MPG

• Mean: 24 MPG, Standard Deviation: 4.8 MPG

• Mean: 24 MPG, Standard Deviation: 4 MPG

Mrs. Day decides to curve her Statistics scores. The mean of the scores was a 71 with a standard deviation of 3 points. She uses the curve: new score = 1.1(old score) + 10. What would be the new score of a student that scored a 76?

• 83.6

• 93.6

• 86.6

• 96.6

Jesse tracks his number of miles run for the past week and finds that he runs an average of 5.3 miles per day with a standard deviation of 1.1 miles. He makes it a goal to improve that by 1.5 miles per day. What would he expect his new mean and standard deviation of miles run per day to be?

• 6.8 miles mean, 1.1 miles standard deviation

• 5.3 miles mean, 2.6 miles standard deviation

• 6.8 miles mean, 2.6 miles standard deviation

• 7.0 miles mean, 1.1 miles standard deviation