Question

When designing motorcycle helmets, the breadth of a person’s head must be considered. Men have head breadths that are normally distributed with a mean of 6.0 inches and a standard deviation of 1.0 inches. If one male is randomly selected, what is the probability that his head breadth is less than 6.2 inches?

Answer 1

Answer:

57.93%

Step-by-step explanation:

We have been given that men have head breadths that are normally distributed with a mean of 6.0 inches and a standard deviation of 1.0 inches. We are asked to find the probability that a man's breadth is less than 6.2 inches.

First of all, we will find z-score corresponding to sample score of 6.2 as:

$z=\frac{x-\mu}{\sigma}$, where,

z = Z-score,

x = Sample score,

$\mu$ = Mean,

$\sigma$ = Standard deviation.

Upon substituting our given values in z-score formula, we will get:

$z=\frac{6.2-6.0}{1.0}$

$z=\frac{0.2}{1.0}$

$z=0.2$

Now, we need to find the probability that a z-score is less than 0.2.

Using normal distribution table, we will get:

$P(z$

$0.57926\approx 57.926\%\approx 57.93\%$

Therefore, the probability that a male's head breadth is less than 6.2 inches, would be approximately 57.93%.