Question

To control pollination, pollen-producing flowers are often removed from the top of corn in a process called detasseling. The hourly rates for detasselers in Iowa are roughly normally distributed, with a mean of $12/hr and a standard deviation of $2/hr.

What are the z-scores for a detasseler making $13 and $17 an hour?

z13 = 0.9, z17 = 1.25

z13 = 0.5, z17 = 1.25

z13 = 0.5, z17 = 2.5

Answer 1

Answer: Last option

$Z_ {13} = 0.5,\ Z_ {17} = 2.5$

Step-by-step explanation:

The z-scores give us information about how many standard deviations from the mean the data are. This difference can be negative, if the data are n deviations to the left of the mean, or it can be positive if the data are n deviations to the right of the mean.

To calculate the Z scores, we calculate the difference between the value of the data and the mean and then divide this difference by the standard deviation.

so  

$Z = \frac{x- \mu}{\sigma}$.

Where x is the value of the data, μ is the mean and σ is the standard deviation

In this case :

μ = 12 $/h

$\sigma$ = 2 $/h

We need to calculate the Z-scores for $x = 17$ and $x = 13$

Then for $x = 17$:

$Z_{17} = \frac{17-12}{2}$.

$Z_{17} = 2.5$

Then for $x = 13$:

$Z_{13} = \frac{13-12}{2}$.

$Z_{13} = 0.5$

Therefore the answer is:

$Z_ {13} = 0.5,\ Z_ {17} = 2.5$

Answer 2

Answer:

C

second part:

69%

99%

30%

Step-by-step explanation: