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 not enough information 1106 to 1150 pounds

Answer 1

Approximately 95% of the molds filled by the machine will hold weights in the interval from 1106 to 1194 pounds, calculated by finding the range within two standard deviations from the mean in a normal distribution.

Step-by-step explanation:

The question you've asked refers to determining the interval within which approximately 95% of the concrete mold weights filled by a machine will fall if the weights follow a normal distribution with a mean of 1150 pounds and a standard deviation of 22 pounds. In a normal distribution, approximately 95% of data falls within two standard deviations of the mean. By calculating this interval, you can find the range where about 95% of the mold weights are expected to lie.

To find this interval, we follow these steps:

1. Calculate the lower bound: Mean - 2(Standard Deviation) = 1150 - 2(22)
2. Calculate the upper bound: Mean + 2(Standard Deviation) = 1150 + 2(22)
3. Combine these values to get the interval within which approximately 95% of the weights should fall.

Thus:

Lower bound = 1150 - 44

= 1106 pounds

Upper bound = 1150 + 44

= 1194 pounds

The interval within which approximately 95% of the molds filled by this machine will hold weights is from 1106 to 1194 pounds.