Question

1. resting heart rates for adult athletes, in beats per minute, follow a normal distribution. tatums resting heart rate is such that 75% of athletes have higher heart rates than she does. this means that tatums heart rate is approximately how many standard deviations away from the mean?

a. 0.5
b. 0.7
c. 1.0
d. 0.6
e. this question cannot be answered without knowing the mean and standard deviation of the distribution.

Explanation:

Step1: Find the percentile of Tatum's heart - rate

If 75% of athletes have higher heart rates than Tatum, then Tatum's heart - rate is at the 25th percentile. That is, $P(X < x_T)=0.25$, where $x_T$ is Tatum's heart - rate.

Step2: Use the standard normal distribution table (z - table)

The standard normal distribution table gives the cumulative probability $P(Z < z)$ for a standard normal random variable $Z$. We need to find the $z$ - score corresponding to a cumulative probability of 0.25. Looking up in the standard normal distribution table, the $z$ - score corresponding to a cumulative probability of 0.25 is approximately $z=- 0.6745\approx - 0.7$. The absolute value of the $z$ - score represents the number of standard deviations away from the mean.

Answer:

B. 0.7