Question

Suppose a simple random sample of size nequals49 is obtained from a population with mu equals 78 and sigma equals 28.

​(a) Describe the sampling distribution of x overbar.
​(b) What is Upper P (x overbar greater than 83.8 )​? ​
(c) What is Upper P (x overbar less than or equals 69.6 )​? ​
(d) What is Upper P (75.8 less than x overbar less than 88 )​?

Answer 1

0.0735,0.0179,0.7026

Explanation:

Given that a simple random sample of size nequals 49 is obtained from a population with mu equals 78 and sigma equals 28.

Sample size = 49

Population mean = 78

Population std deviation = 28

Std error of sample mean =
`(\sigma)/(√(n) ) \\=4`

a)
`\bar x`: N(78, 4)

b)
`P(\bar x >83.8)\\=0.0735`

(by converting to Z and finding value from Z table)

c) P (x overbar less than or equals 69.6 )​

=
`P(\bar x \leq 69.6)\\=0.0179`

d) P (75.8 less than x overbar less than 88 )

=
`P(75.8<X<88)\\= 0.9938-0.2912\\=0.7026`