Question

1. the mean temperature in glen falls for the month of february is 23 degrees with a standard deviation of 4.2 degrees. what is the z-score for a temperature of 17 degrees? a. 1 b. 1.43 c. -1.43 d. 11.5 19. 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 on 0.3 seconds. what is the z-score for a player who runs a time of 5.6 seconds? a. -1.33 b. 0.88 c. 1.02 d. 1.33 20. the mean number of accidents a week at a company is 6.4 with a standard deviation of 1.5. what proportion of weeks would you expect to have less than 5 accidents? a. 0.6915 b. 0.1762 c. 0.8238 d. -0.93

Explanation:

Step1: Recall the z - score formula

The z - score formula is \(z=\frac{x-\mu}{\sigma}\), where \(x\) is the data point, \(\mu\) is the mean, and \(\sigma\) is the standard deviation.

Step2: Calculate the z - score for the 40 - yard sprint problem

Given \(\mu = 5.2\), \(\sigma=0.3\), and \(x = 5.6\).
Substitute into the formula: \(z=\frac{5.6 - 5.2}{0.3}=\frac{0.4}{0.3}\approx1.33\)

Answer:

D. 1.33