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?

a. z13=0.9,z17 =1.25
b. z13=0.5,z17=1.25
c. z13 =0.5,z17 =2.5
d. The probability of a detasseler making less than $13/hr is given by p(z<0.5)≈%.

Answer 1

A detasseler making $13 an hour has a z-score of 0.5, and one making $17 an hour has a z-score of 2.5, indicating their wages are above and far above the mean, respectively.

Step-by-step explanation:

To calculate the z-scores for detasselers making $13 and $17 an hour when the mean hourly rate is $12 and the standard deviation is $2, we use the formula:

Z = (X - µ) / σ

Where X is the individual value, µ is the mean, and σ is the standard deviation.

For $13/hr:

Z = ($13 - $12) / $2 = $1 / $2 = 0.5

For $17/hr:

Z = ($17 - $12) / $2 = $5 / $2 = 2.5

Therefore, the detasseler making $13 an hour has a z-score of 0.5, and the detasseler making $17 an hour has a z-score of 2.5. This means option 'c' is the correct answer.