Answer:
The proportions of WNBA basketballs smaller than 29.1 inches is 0.8413.
Step-by-step 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.
[tex]z=\frac{x-\mu}{\sigma}[/tex]
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:
[tex]P(X<29.1)=P(\frac{X-\mu}{\sigma}<\frac{29.1-29.0}{0.01})[/tex]
[tex]=P(Z<1)\\=0.84134\\\approx0.8413[/tex]
Thus, the proportions of WNBA basketballs smaller than 29.1 inches is 0.8413.
