Sample Distribution Question

Question

Let x be a continuous random variable that has a normal distribution with μ=73
and  σ=18.
Assuming n N≤ 0.05, find the probability that the sample mean,
x ,for a random sample of 19 taken from this population will be between 70.8 and 81.7
.

Answer 1

 

    Z = (sample mean - population mean)/ ( stddev/sqrt(N))

 

   

 

   zLow = (70.8 - 73)/(18/sqrt(19)) = 0.53275

 

 zHigh = (81.7 - 73)/(18/sqrt(19)) = 2.1068

 

0.9828 - 1/2 +  0.7019 - 1/2 = 0.6847