Using the **normal **distribution, it is found that:

**a)** The pilot is at the **72th percentile.**

**b) 19.13%** of pilots are unable to fly.

<h3>Normal Probability Distribution</h3>

The **z-score **of a **measure X **of a normally distributed variable with **mean ** and** standard deviation** is given by:

- The z-score
**measures **how many standard deviations the measure is above or below the mean.

- Looking at the z-score table, the
**p-value** associated with this z-score is found, which is the **percentile **of X.

The **mean **and the** standard deviation** are given, respectively, by:

.

Item **a**:

The **percentile **is the <u>p-value of Z when X = 74.2</u>, hence:

Z = 0.59

Z = 0.59 has a p-value of 0.7224.

72th percentile.

Item **b**:

The **proportion that is able to fly **is the <u>p-value of Z when X = 78 subtracted by the p-value of Z when X = 70</u>, hence:

**X = 78:**

Z = 2

Z = 2 has a p-value of 0.9772.

**X = 70:**

Z = -0.96

Z = -0.96 has a p-value of 0.1685.

0.9772 - 0.1685 = 0.8087 = 80.87%.

Hence the **percentage that is unable to fly** is:

100 - 80.87 = 19.13%.

More can be learned about the **normal distribution **at brainly.com/question/4079902

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