Question

question 2
suppose the time to complete a 200 - meter backstroke swim for female competitive swimmers is normally distributed with a mean μ = 141 seconds and a standard deviation σ = 7 seconds.
what is the completion time for the 200 - meter backstroke for a female with a z - score of - 1.64? (round answer to 1 decimal place.)
a. 152.5
b. 130.8
c. 141.0
d. 129.5

Explanation:

Step1: Recall z - score formula

The z - score formula is $z=\frac{x-\mu}{\sigma}$, where $z$ is the z - score, $x$ is the value from the data set, $\mu$ is the mean, and $\sigma$ is the standard deviation. We want to solve for $x$. Rearranging the formula gives $x=\mu + z\sigma$.

Step2: Substitute given values

We are given that $\mu = 141$, $z=-1.64$, and $\sigma = 7$. Substitute these values into the formula: $x=141+(-1.64)\times7$.

Step3: Perform calculation

First, calculate $(-1.64)\times7=-11.48$. Then, $x = 141- 11.48=129.52$.

Step4: Round the result

Rounding $129.52$ to one decimal place gives $129.5$.

Answer:

D. 129.5