Question

Adult female height is normally distributed with a mean of 65.3 inches and a standard deviation of 2.32 inches. a) If an adult female is randomly selected, what is the probability that the adult female has a height less than 61.3 inches? Round your final answer to four decimal places

Answer 1

Answer:

0.0423 is the probability that the adult female has a height less than 61.3 inches.

Step-by-step explanation:

We are given the following information in the question:

Mean, μ = 65.3 inches

Standard Deviation, σ = 2.32 inches

We are given that the distribution of adult female height is a bell shaped distribution that is a normal distribution.

Formula:

$z_{score} = \displaystyle\frac{x-\mu}{\sigma}$

P(adult female has a height less than 61.3 inches)

$P( x < 61.3) = P( z < \displaystyle\frac{61.3 - 65.3}{2.32}) = P(z < -1.7241)$

Calculation the value from standard normal z table, we have,  

$P(x < 61.3) =0.0423 = 4.23\%$

0.0423 is the probability that the adult female has a height less than 61.3 inches.