Question

Find P(46≤x¯≤54) for a random sample of size 33 with a mean of 51 and a standard deviation of 10.   (Round your answer to four decimal places.)

True or False: The standard error of the mean, σx¯, is always larger than the population standard deviation σ.

Answer 1

Solution :

Given that,

mean = = 51

standard deviation = = 10

n = 33

= 51

= / n = 10 33= 1.7408

P (46 54)

P ( 46 - 51 / 1.7408) ( - /) ( 54 - 51 / 1.7408 )

P ( - 5 / 1.7408 z 3 / 1.7408 )

P (-2.87 z 1.72 )

P ( z 1.72 ) - P ( z -2.87)

Using z table

= 0.9573 - 0.0021

= 0.9552

Probability = 0.9552

False

The standard error of the mean, σx¯, is always larger than the population standard deviation σ