Question

The circumferences of WNBA basketballs follow a normal distribution where mean = 29.0 ; and standard deviation = 0.1 inches.

What proportion of WNBA basketballs are SMALLER than 29.1?

Answer 1

The proportions of WNBA basketballs smaller than 29.1 inches is 0.8413.

Explanation:

Let the random variable X be defined as the circumferences of WNBA basketballs.

The mean of the random variable X is, μ = 29.0 inches and the standard deviation is, σ = 0.10 inches.

The random variable X follows a Normal distribution.

To compute the probability of a normally distributed random variable we must convert the raw score (X) to z-scores.

`z=(x-\mu)/(\sigma)`

The z-scores follows a Standard normal distribution, i.e. N (0, 1).

Compute the probability of circumferences of WNBA basketballs smaller than 29.1 inches as follows:

`P(X<29.1)=P((X-\mu)/(\sigma)<(29.1-29.0)/(0.01))`

`=P(Z<1)\\=0.84134\\\approx0.8413`

Thus, the proportions of WNBA basketballs smaller than 29.1 inches is 0.8413.