Question

a random sample of 25 is collected for a continuoue random variable x. the observed sample mean is 172.5 and the sample deviation is 15.4.

a. construct a95% confidence interval for the population mean

b. can the population mean of X, ux be equal to 160?

c. what is the probability that ux is equal or less than 178.86

d. what about 166.14

e. what is the probabilith that ux=172.5?

Answer 1

t value at 95% = 2.0639

CI = 172.5+ /- 2.0639 *(15.4/sqrt(25))
= (166.1432,178.8568)

b)
yes

c)

P(x < 178.86)
= P(z < (178.86 - 172.5)/(15.4/sqrt(25))
= P(z < 2.0649)
= 0.9805

d)

P(x < 166.14)
= P(z < (166.14 - 172.5)/(15.4/sqrt(25))
= P(z < -2.0649)
= 0.0195

e)

P(x = 172.5)
= P(z = (172.5- 172.5)/(15.4/sqrt(25))
= P(z =0)
= 0.05