For this question the average height of adult women is 63.7” with a sigma of 2.9”.  The US Navy requires that fighter pilots have heights of between 62 and 78 inches.  Find the approximate percentage or women who qualify to be fighter pilots.  HINT:  Drawing a distribution curve may help.

72%

Step-by-step explanation:

For this question the average height of adult women is 63.7” with a σ of 2.9”.  The US Navy requires that fighter pilots have heights of between 62 and 78 inches.  Find the approximate percentage or women who qualify to be fighter pilots.  HINT:  Drawing a distribution curve may help.

Find the z-scores.

z = (x − μ) / σ

z₁ = (62 − 63.7) / 2.9

z₁ = -0.586

z₂ = (78 − 63.7) / 2.9

z₂ = 4.93

Use a chart or calculator to find the probability.

P(-0.586 < Z < 4.93) = P(Z < 4.93) − P(Z < -0.586)

P(-0.586 < Z < 4.93) = 1.000 − 0.279

P(-0.586 < Z < 4.93) = 0.721

Approximately 72% of women will qualify.

If the Navy changes its height requirement to include all but the shortest and tallest 3% of the female population, what would the new height requirements for women be? HINT:  Drawing a distribution curve may help. Also, rounding is suggested.

In this case, we work in reverse.  Use a chart or calculator to find the z-score for each probability.

P(Z < z₁) = 0.03

z₁ = -1.881

P(Z > z₂) = 0.03

P(Z < z₂) = 0.97

z₂ = 1.881

Now find the heights associated with those z-scores.

z = (x − μ) / σ

-1.881 = (x₁ − 63.7) / 2.9

x₁ = 58.2

1.881 = (x₂ − 63.7) / 2.9

x₂ = 69.2

The new height requirement is between 58.2" and 69.2".

36 girls

step-by-step explanation:

the 48 boys is 4 parts of the ratio

divide 48 by 4 to obtain one part of the ratio

= 12 ← 1 part of the ratio

3 parts = 3 × 12 = 36 ← number of girls