Clyde clement wants to analyze a shipment of bags of cement. he knows the weight of the bags is normally distributed so he can use the standard normal distribution. he measures the weight of 600 randomly selected bags in the shipment. next, he calculates the mean and standard deviation of their weights. the mean is 50 lbs. and the standard deviation is 1.5 lbs. clyde uses the normal distribution table to calculate the number of bags in each segment of the distribution.

Given that Clyde Clement wants to analyze a shipment of bags of cement. That he knows the weight of the bags is normally distributed so he can use the standard normal distribution. That he measured the weight of 600 randomly selected bags in the shipment. That he calculated the mean and standard deviation of their weights as 50 lbs and 1.5 lbs respectively.

To calculate the number of bags in each segment of the distribution we use the normal distribution table.

Case 1: Between -2 and -1 standard deviations.
The mean weight will be -2(1.5) + 50 to -1(1.5) + 50 = -3 + 50 to -1.5 + 50 = 47 lbs to 48.5 lbs
From table, the probability of between -2 and -1 standard deviations = P(-1) - P(-2) = (1 - P(1)) - (1 - P(2)) = P(2) - P(1) = 0.97725 - 0.84134 = 0.13591 ≈ 13.6%
Number of bags out of 600 = 0.13591 x 600 ≈ 82 bags

Case 2: Between -1 and 0 standard deviations.
The mean weight will be -1(1.5) + 50 to 0(1.5) + 50 = -1.5 + 50 to 0 + 50 = 48.5 lbs to 50 lbs
From table, the probability of between -1 and 0 standard deviations = P(0) - P(-1) = P(0) - (1 - P(1)) = P(0) + P(1) - 1 = 0.5 + 0.84134 - 1 = 0.34134 ≈ 34.1%
Number of bags out of 600 = 0.34134 x 600 ≈ 205 bags

Case 3: Between 0 and 1 standard deviations.
The mean weight will be 0(1.5) + 50 to 1(1.5) + 50 = 0 + 50 to 1.5 + 50 = 50 lbs to 51.5 lbs
From table, the probability of between 0 and 1 standard deviations = P(1) - P(0) = 0.84134 - 0.5 = 0.34134 ≈ 34.1%
Number of bags out of 600 = 0.34134 x 600 ≈ 205 bags

Case 4: Between 1 and 2 standard deviations.
The mean weight will be 1(1.5) + 50 to 2(1.5) + 50 = 1.5 + 50 to 3 + 50 = 51.5 lbs to 53 lbs
From table, the probability of between 1 and 2 standard deviations = P(2) - P(1) = 0.97725 - 0.84134 = 0.13591 ≈ 13.6%
Number of bags out of 600 = 0.13591 x 600 ≈ 82 bags