# Thread: The Sampling distribution of the sample mean

1. ## The Sampling distribution of the sample mean

A bran of water-softener salt comes in packages marked "net weight 40lb"
The company packages the salt claims that the bags contain an average of 40 lb. of salt and the standard deviation of the weights is 1.5 lb. Assume the weights are normally distributed.

Obtain the probability that the weight of one randomly selected bag of water-softner salt will be 39lb or less, if the companys clain is true.

Please explain how to do this. Thanks

2. Originally Posted by l0v3n
A bran of water-softener salt comes in packages marked "net weight 40lb"
The company packages the salt claims that the bags contain an average of 40 lb. of salt and the standard deviation of the weights is 1.5 lb. Assume the weights are normally distributed.

Obtain the probability that the weight of one randomly selected bag of water-softner salt will be 39lb or less, if the companys clain is true.

Please explain how to do this. Thanks
Let X be the random variable amount of salt (measured in lb) in bag.

X ~ Normal $\, (\mu = 40, \, \sigma = 1.5)$.

You need to calculate Pr (X < 39).

Without knowing you're method for calculating probabilities for a normal distribution (tables, calculator etc.), that's as far as I go ....