Distributions and Percentiles

The 40 yards sprint times for a soccer team are found to be normally distributed with a mean of 5.2 seconds and a standard deviation of 0.3 seconds.  What is the z-score for a player who runs a time of 4.8 seconds?

• -1.33
• 1.33
• 0.88
• 1.02

The mean number of accidents a week at a company is N(6.4, 1.5) What proportion of weeks would you expect to have less than 5 accidents?

• 0.6915
• 0.1762
• 0.8238
• -0.93

The GPA of students in a course at UC Davis is approximately normal with a mean of 3.2 with a standard deviation of 0.3. What percent of students in the course have a GPA between  2.9 and 3.8? 

• 81.5%
• 47.5%
• 68%
• Cannot be determined

Tags

CCSS.HSS.ID.A.4

Which of the following statements is/are true about the standard normal distribution?
I. It is bell-shaped.
II. It is unimodal.
III. It is uniform
IV. The mean is 0 and the standard deviation is 1.

• II, III, IV only 
• I and IV only
• None of the statements
• I, II, IV

Suppose a student takes a standardized test measuring college level skills. Scores on the test are normally distributed with a mean of 500 and a standard deviation of 100. Which of the following is NOT true about the distribution?

• Scores lower than 300 and higher than 700 could be considered outliers.
• 68% of scores are between 300 and 700. 
• The 16th percentile is 400.
• 2.5% of scores are higher than 700. 

In a survey of men in the United States (ages 20-29), the mean height was 69.6 inches with a standard deviation of 3.0 inches. Find the minimum height in the top 22%.

• 69.37 in 
• 67.58 in 
• 71.92 in 
• Cannot Determine the Answer :(

Find the z-score that corresponds to the percentile P_95.

• -0.06
• 1.14
• -1.41
• 1.64

The weight of bags of pretzels are normally distributed with a mean of 150 gr. and a standard deviation of 5 gr. Bags in the upper 4.5% are too heavy and the bags in the lower 5% do not meet the minimum weight requirement so they  must be repackaged. What is the range of weight for a pretzel bag that does not need to be repackaged?

• 141.78 - 158.48 gr 
• 148.48 - 151.78 gr
• 140.87 - 156.84 gr
• Cannot be determined