Question

According to a research institution, the average hotel price in a certain year was $100 21 Assume the population standard deviation is $17 00 and that a random sample of 4 hotels was selected Complete parts a through d befow a, calculate the standard error of the mean Round to two decimal places as needed ) b. What is the probability that the sample mean will be less than $1027 X < $102) : (Round to four decimal places as needed ) c. What is the probability that the sample mean will be more than $104? (x> $104) Round to four decimal places as needed ) d. What is the probability that the sample mean will be between $99 and $100? Round to four decimal places as needed)

Answer 1

a) Standard error of mean

b)

$P(\overline{X}<102)=P\left ( Z<\frac{102-100.21}{2.56} \right )$

P(Z < 0.70) 0.5+0.2580 = 0.7580

c)

$P(\overline{X}>104)=P\left ( Z>\frac{104-100.21}{2.56} \right )$

d)

$P(99\leq \overline{x}\leq 100) =P\left ( \frac{99-100.21}{2.56}\leq Z\leq \frac{100-100.21}{2.56} \right )$

$P(-0.47\leq Z\leq -0.08) =0.1808-0.0319 =0.1489$