Question

Assume that the weight of hamsters is Normally distributed with μ = 1 lbs and σ = 0.25 lbs. Suppose I randomly select 6 hamsters.

(a) What is the shape of the sampling distribution of the sample mean? -Unknown, Exactly Normal, or Approximately Normal

(b) What is P(X < 1.1)? (Use 3 decimal places) *Can you please explain how to find this value too rather than just give the answer?

Answer 1

Sol:

since the sample is from normal distribution

According to centrral limit theorem samplie(n=6)follows approximately normal distribuion

with sample mean=xbar=Mu=1

sample standard deviation=s=sigma/sqrt(n)=0.25/sqrt(6)= 0.1020621

Approximately Normal

(b) What is P(X < 1.1)? (Use 3 decimal places) *Can you please explain how to find this value too rather than just give the answer?

Z=x-mean/sd

z=1.1-1/0.1020621

z= 0.9797956

P(Z<0.9798)

From standard normal table,

=0.8364

0.836