Question

The height of 18-year-old men are approximately normally distributed, with mean of 68 inches and a standard deviation of 3 inches. what is the probability that an 18-year-old man selected at random is between 67 and 69 inches tall? round your answer to the nearest thousandths place (3 places).the height of 18-year-old men are approximately normally distributed, with mean of 68 inches and a standard deviation of 3 inches. what is the probability that an 18-year-old man selected at random is between 67 and 69 inches tall? round your answer to the nearest thousandths place (3 places).

Answer 1

The bell curve below shows the location of the mean and the two values of X; 67 and 69

The area under the curve equals to 1 (as probability equals to one)

We want the area between X=67 and X=69

We first need to find the z-score of X=67 and X=69

z-score of X=67 is given by $\frac{67-68}{3} = -0.33$
z-score of X=69 is given by $\frac{69-68}{3}=0.33$

The area between z-score -0.33 and 0.33 is given by 
P(Z<0.33) - P(Z<-0.33)

We need to read off the z-table to find the value of P(Z<0.33) and P(Z<-0.33).
A screenshot of the z-table is shown below

P(Z<-0.33) = 0.3707
P(Z<0.33) = 0.6293

Hence, the probability that an 18-year old man  selected at random is between 67 and 69 inches tall is 0.6293-0.3707=0.2586 or 25.86%