Question

question 2
suppose the time to complete a 200 - meter backstroke swim for female competitive swimmers is normally distributed with a mean $mu = 141$ seconds and a standard deviation $sigma = 7$ 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. 141.0
b. 152.5
c. 129.5
d. 130.8

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 find $x$, so we can re - arrange the formula to $x=\mu + z\sigma$.

Step2: Substitute given values

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

$$\begin{align*} x&=141+(-1.64)\times7\\ &=141 - 11.48\\ &=129.52 \end{align*}$$

\]

Step3: Round the result

Rounding 129.52 to 1 decimal place gives 129.5.

Answer:

C. 129.5