Question

Engineers must consider the breadths of male heads when designing motorcycle helmets. men have head breadths that are normally distributed with a mean of 6.0 in and a standard deviation of 1.0 in. (based on anthropometric survey data from gordon, churchill, et al.). if one male is randomly selected, find the probability that his head breadth is less than 6.2 in. use 4 decimals for your answer.

Answer 1

The probability is 0.5793.

We calculate this using a z-score.  Z-scores are found by subtracting our data point from the mean, then dividing by the standard deviation:

z = (6.2-6)/(1.0) = 0.2

We then look up the score in a table (http://www.z-table.com).

P(X<6.2) = P(z<0.2) = 0.5793 from the table.

Answer 2

Answer: 0.9772 (the answer above wasn't the right one;)