Answer:
72%
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".