Suppose a simple random sample of size nequals45 is obtained from a population with muequals64 and sigmaequals14. (a) What must be true regarding the distribution of the population in order to use the normal model to compute probabilities regarding the sample mean? Assuming the normal model can be used, describe the sampling distribution x overbar. (b) Assuming the normal model can be used, determine P(x overbarless than68.1). (c) Assuming the normal model can be used, determine P(x overbargreater than or equals66.3).
Accepted Solution
A:
Answer:Step-by-step explanation:Given that sample size = n=45mu = 64 and sigma =14a) Sample mean will follow a normal distribution irrespective of the original distributions providedi) samples are randomly drawn ii) samples represent the populationiii) Sample size is sufficiently largeb) Here we have sample std dev= [tex]\frac{\sigma}{\sqrt{n} } \\=\frac{14}{\sqrt{45} } \\=2.09[/tex][tex]P(X bar>68.1) = P(Z>\frac{68.1-64}{2.09} \\=P(Z>1.96)\\=0.25[/tex]c) [tex]P(X bar>66.3) = P(Z>\frac{66.3-64}{2.09} \\=P(Z>1.10)\\=0.136[/tex]