Question

The compressive strength of samples of cement can be modeled by a normal distribution with a mean of 6000 kilograms per square centimeter and a standard deviation of 100 kilograms per square centime.

What strength is exceeded by 90% of the samples?

Answer 1

To find the strength exceeded by 90% of the samples, use the mean and standard deviation of the normal distribution and find the corresponding z-score. Then, use the z-score to calculate the strength value. In this case, the strength exceeded by 90% of the samples is 6138 kilograms per square centimeter.

Step-by-step explanation:

To find the strength exceeded by 90% of the samples, we need to find the z-score corresponding to 90% on the normal distribution. The z-score represents the number of standard deviations away from the mean. We can use a standard normal distribution table or a statistical calculator to find that the z-score for 90% is approximately 1.28.

Next, we can use the formula for converting a z-score to an x-value (strength in this case) using the mean and standard deviation:

x = mean + (z * standard deviation)

Plugging in the values, we get:

x = 6000 + (1.28 * 100) = 6138 kilograms per square centimeter