Question

The weights of adobe bricks used for construction are normally distributed with a mean of 3 pounds and a standard deviation of 0.25 pound. Assume that the weights of the bricks are independent and that a random sample of 28 bricks is selected. Round your answers to four decimal places (e.g. 98.7654). (a) What is the probability that all the bricks in the sample exceed 2.75 pounds? (b) What is the probability that the heaviest brick in the sample exceeds 3.75 pounds?

Answer 1

Answer:  a) 0.8413, b) 0.9987.

Step-by-step explanation:

Since we have given that

Mean = 3 pounds

Standard deviation = 0.25 pounds

n = 28 bricks

So, (a) What is the probability that all the bricks in the sample exceed 2.75 pounds?

$P(X>2.75)\\\\=P(z>\dfrac{2.75-3}{0.25}\\\\=P(z>\dfrac{-0.25}{0.25})\\\\=P(z>-1)\\\\=0.8413$

b) What is the probability that the heaviest brick in the sample exceeds 3.75 pounds?

$P(X>3.75)\\\\=P(z>\dfrac{3.75-3}{0.25})\\\\=P(z>\dfrac{0.75}{0.25})\\\\=P(z>3)\\\\=0.9987$

Hence, a) 0.8413, b) 0.9987.