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?

a) 1084 to 1216 pounds
b) 1106 to 1194 pounds
c) 1106 to 1150 pounds
d) 1128 to 1172 pounds

Answer 1

The interval that contains approximately 95% of the molds' weights filled by the machine is 1106 to 1194 pounds, following the empirical rule for a normal distribution, which corresponds to option b) of the choices provided.

Step-by-step explanation:

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. To find the interval that contains approximately 95% of the molds filled by this machine, we need to use the empirical rule which states that about 95% of the data in a normal distribution falls within ±2 standard deviations of the mean.

To calculate the interval:

1. Start with the mean: 1150 pounds.
2. Calculate the lower limit by subtracting 2 standard deviations from the mean: 1150 - (2 × 22) = 1150 - 44 = 1106 pounds.
3. Calculate the upper limit by adding 2 standard deviations to the mean: 1150 + (2 × 22) = 1150 + 44 = 1194 pounds.

Therefore, approximately 95% of the molds filled by this machine will hold weights in the interval 1106 to 1194 pounds.

The correct answer is option b) 1106 to 1194 pounds.