Question

A regulation baseball can weigh no more than 149 grams. A factory produces baseballs with weights that are normally distributed with a mean of 146 grams and a standard deviation of 2.3 grams.

Answer 1

Answer:

0.9032

Step-by-step explanation:

Given that:

mean (μ) = 146 grams and standard deviation (σ) = 2.3 grams

The z score is a measurement used in statistics to calculate how far a value is from the mean in a normal distribution. The z score is given as:

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

For the baseball not to weigh more than 149 grams i.e x = 149 g

$z=\frac{x-\mu}{\sigma}=\frac{149-146}{2.3} =1.30$

From the probability distribution table, P(x < 149) = P(z < 1.30) = 0.9032 = 90.32%