The upper leg length of 20 to 29-year-old males is normally distributed with a mean length of 43.7 cm and a standard deviation of 4.2 cm. a random sample of 9 males who are 20 to 29 years old is obtained. what it the probability that the mean leg length is less than 20 cm? 0.1894 pratically 0 0.2134 0.7898

Given:

μ = 43.7 cm, the population mean

σ = 4.2 cm, the population standard deviation.

We want to test against the population statistics with

n = 9, the sample size,

x = 20 cm, the random variable.

We want to find P (x < 20).

Calculate the z-score.

z = (x - μ) / σ

= (20 - 43.7) / 4.2

= - 5.643

From the standard tables, obtain

P (z < - 5.643) = 0 (actually about 8.5 x 10⁻⁹)

Answer: Practically zero.