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

C

second part:

69%

99%

30%

Explanation:

Answer 2

Answer: Last option

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

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 = (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) = (17-12)/(2)`.

`Z_(17) = 2.5`

Then for
`x = 13`:

`Z_(13) = (13-12)/(2)`.

`Z_(13) = 0.5`

Therefore the answer is:

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