Question

in a factory, the weight of the concrete poured into a mold by a machine follows a normal distribution with a mean of 1150 pounds and a standard deviation of 22 pounds. approximately 95% of molds filled by this machine will hold weights in what interval? 1106 to 1194 pounds 1084 to 1216 pounds 1128 to 1172 pounds 1106 to 1150 pounds

Explanation:

Step1: Recall the empirical rule for normal distribution

For a normal distribution, approximately 95% of the data lies within \( \mu - 2\sigma \) and \( \mu + 2\sigma \), where \( \mu \) is the mean and \( \sigma \) is the standard deviation.

Step2: Identify \( \mu \) and \( \sigma \)

Given \( \mu = 1150 \) pounds and \( \sigma = 22 \) pounds.

Step3: Calculate the lower bound

Lower bound \( = \mu - 2\sigma = 1150 - 2\times22 = 1150 - 44 = 1106 \)

Step4: Calculate the upper bound

Upper bound \( = \mu + 2\sigma = 1150 + 2\times22 = 1150 + 44 = 1194 \)

Answer:

1106 to 1194 pounds