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. (a) If a baseball produced by the factory is randomly selected, what is the probability that it is within regulation weight? (b) The baseballs are shipped in boxes of 16. What is the probability that at least 15 of the 16 baseballs in a pack are within regulation weight? (c) The factory will not ship a box of 16 if the average weight of the baseballs in the box exceeds 147 grams. What is the probability that a pack of 16 baseballs would have an average weight of more than 147 grams?

Answer 1

90.32% probability that it is within regulation weight

Answer 2

(a) The probability that a selected ball is within regulation weight is 84%.

(b) Probability of at least 15 of 16 balls withing regulation weight is 10.5%.

(c) The probability of average weight of more than 147 grams is 66.67%.

Probability of baseball within regulation weight

The probability of baseball within regulation weight is calculated as follows;

one standard deviation above the mean = M + d = 84%

two standard deviation above the mean = M + 2d = 98%

where;

• M is the mean
• d is standard deviation

one standard deviation above the mean = 146 g + 2.3 g = 148.3 g

two standard deviation above the mean = 146 g + 2(2.3g) = 150.6 g

150.6 g is above regulation weight.

Thus, when a baseball is randomly selected, the probability that it is within regulation weight is 84%.

Probability of  at least 15 balls out of 16 balls;

outcome = (15, 16) = 2 outcome

P = 2/16 x 84%

P = 10.5%

Probability of average weight of more than 147 grams

Mean of the distribution = 146 = 50%

Average weight more than 147g = ?

Maximum weight of 149g = 100%

(147 - 146)/(149 - 146) = (? - 50)/(100 - 50)

0.333 = (? - 50)/(50)

50(0.333) = ? - 50

? = 50(0.333)  + 50

? = 66.67%

Learn more about probability here: https://brainly.com/question/24756209