Question

1. A food company that sells salmon to stores asserts the weights of the salmon have a mean of 35 pounds and a standard deviation of 4 pounds.

1. If a large seafood restaurant purchases a random sample of 100 salmon, give the properties (and provide a sketch) for the sampling distribution for the sample mean weight in the purchase.

2. Find the probability the sample mean weight will be at least 34 pounds.

Answer 1

Consider the random variable

X : Weight of the salmon.

From the information

Mu= mean weight of salmon = 35 punds

sigma = Standard deviation = 4 pounds.

a) n = sample size = 100

Xbar : Mean weight of 100 sample.

Since n is large, the distribution of sample mean approches to normal distribution with

i.e.

Properties.

i) The frequency curve is bell shaped.

ii) The distribution is symmetric about mean = 35.

iii) The distribution is mesokurtic.

Frequency Curve :

b) P ( Sample mean weight weight will be at least 34 pounds) = P ( Xbar > = 34)

From normal probability table

P ( Sample mean weight weight will be at least 34 pounds) = 0.9938.