Question

(1 point) The temperature at any random location in a kiln used in the manufacture of bricks is normally distributed with amean of 1025 and a standard deviation of 40 degrees.If bricks are fired at a temperature above 1115, they will crack and must be disposed of. If the bricks are placed randomlythroughout the kiln, the proportion of bricks that crack during the firing process is closest to(Note: Please enter your answer in decimal form. For example, 5.02% should be entered as 0.0502.)

Answer 1

Since the temperatures are normally distributed and the population standard deviation is known, we would calculate the z score by applying the formula;

z = (x - μ)/σ

where

x represents sample mean

σ represents population standard deviation

μ represents population mean

From the information given,

μ = 1025

σ = 40

x = 1115

z = (1115 - 1025)/40 = 2.25

We want to find P(x > 1115)

P(x > 1115) = 1 - P(x ≤ 1115)

P(x ≤ 1115) is the area to the left of z = 2.25 from the normal distribution table. Thus,

P(x ≤ 1115) = 0.9878

P(x > 1115) = 1 - 0.9878

P(x > 1115) = 0.0122

The proportion of bricks that crack during the firing process is closest to 0.0122