Question

he temperature at any random location in a kiln used in the manufacture of bricks is normally distributed with a mean of 925 and a standard deviation of 60 degrees. If bricks are fired at a temperature above 1150, they will crack and must be disposed of. If the bricks are placed randomly throughout the kiln, the proportion of bricks that crack during the firing process is closest to

Answer 1

The proportion of bricks that crack during the firing process is 0.0001 = 0.01%.

Explanation:

Normal Probability Distribution:

Problems of normal distributions can be solved using the z-score formula.

In a set with mean
`\mu` and standard deviation
`\sigma`, the zscore of a measure X is given by:

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

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.

Mean of 925 and a standard deviation of 60 degrees.

This means that
`\mu = 925, \sigma = 60`

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

This is 1 subtracted by the pvalue of Z when X = 1150. So

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

`Z = (1150 - 925)/(60)`

`Z = 3.75`

`Z = 3.75` has a pvalue of 0.9999

1 - 0.9999 = 0.0001

The proportion of bricks that crack during the firing process is 0.0001 = 0.01%.