Question

The actual weight of a 2-pound sacks of salted peanuts is found to be normally distributed with a mean equal to 2.04 pounds and a standard deviation of 0.25 pounds. Given the information, the probability of a sack weighing more than 2.40 pounds is 0.4251. True or False.​

Answer 1

False

Explanation:

Normal Probability Distribution:

Problems of normal distributions can be solved using the z-score formula.

In a set with mean
`\mu` and standard deviation
`\sigma`, the zscore of a measure X is given by:

`Z = (X - \mu)/(\sigma)`

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.

Mean equal to 2.04 pounds and a standard deviation of 0.25 pounds.

This means that
`\mu = 2.04, \sigma = 0.25`

The probability of a sack weighing more than 2.40 pounds is 0.4251. True or False.​

We have to find 1 subtracted by the vpalue of Z when X = 2.4. So

`Z = (X - \mu)/(\sigma)`

`Z = (2.4 - 2.04)/(0.25)`

`Z = 1.44`

`Z = 1.44` has a pvalue of 0.9251

1 - 0.9251 = 0.0749

The probability is 0.0749, which means that the answer is False.