Answer:
a) A response of 8.9 represents the 92nd percentile.
b) A response of 6.6 represents the 62nd percentile.
c) A response of 4.4 represents the first quartile.
Step-by-step explanation:
We are given the following information in the question:
Mean, μ = 5.9
Standard Deviation, σ = 2.2
We assume that the distribution of response is a bell shaped distribution that is a normal distribution.
Formula:
![z_{score} = \displaystyle\frac{x-\mu}{\sigma}](https://tex.z-dn.net/?f=z_%7Bscore%7D%20%3D%20%5Cdisplaystyle%5Cfrac%7Bx-%5Cmu%7D%7B%5Csigma%7D)
a) We have to find the value of x such that the probability is 0.92
P(X < x)
Calculation the value from standard normal z table, we have,
![P(z](https://tex.z-dn.net/?f=P%28z%3C1.405%29%20%3D%200.92)
A response of 8.9 represents the 92nd percentile.
b) We have to find the value of x such that the probability is 0.62
P(X < x)
Calculation the value from standard normal z table, we have,
![P(z](https://tex.z-dn.net/?f=P%28z%3C0.305%29%20%3D%200.92)
A response of 6.6 represents the 62nd percentile.
c) We have to find the value of x such that the probability is 0.25
P(X < x)
Calculation the value from standard normal z table, we have,
![P(z](https://tex.z-dn.net/?f=P%28z%3C0.305%29%20%3D%20-0.674)
A response of 4.4 represents the first quartile.