Question

20. Using a Z-score table. Fernando is 60 inches tall. The

average height for his age and gender is 68 with a standard
deviation of 10 inches. What percent of his peers are
shorter than him?
a) 46.81%
b) 8%
c) 78.81%
d) 21.19%

Answer 1

The correct option is (d) 21.19%.

Explanation:

Let the random variable X denote the heights of Fernando's peers.

The mean and standard deviation of the random variable X are:

μ = 68 inches

σ = 10 inches

It is provided that Fernando is 60 inches tall.

Compute the value of P (X < 60) as follows:

`P(X<60)=P((X-\mu)/(\sigma)<(60-68)/(10))`

`=P(Z<-0.80)\\=1-P(Z<0.80)\\=1-0.78814\\=0.21186\\\approx 0.2119`

*Use a z-table.

The percentage is, 0.2119 × 100 = 21.19%.

Thus, the percentage of his peers are shorter than Fernando is 21.19%.

The correct option is (d).