Question

The temperature at any random location in a kiln used in the manufacture of bricks is normally distributed with a mean of 1000 and a standard deviation of 50°F. When glazed bricks are put in the oven, if the temperature is below 900°F they will miscolor. If the bricks are placed randomly throughout the kiln, the proportion of glazed bricks that miscolor is closest to Group of answer choices

a. 49.38%.
b. 2.28%.
c. 47.72%.
d. 0.62%.

Answer 1

b. 2.28%.

Explanation:

Mean temperatue (μ) = 1000°F

Standard Deviation (σ) = 50 °F

For any temperature value, X, the z-score is given by:

`z=(X-\mu)/(\sigma)`

For X= 900°F

`z=(900-1000)/(50)\\z=-2.0`

A z-score of -2.0 corresponds to the 2.28-th percentile of a normal distribution. Therefore, the probability that X<900 is:

`P(X<900) = 2.28\%`