Question

A population has a mean of 50 and a standard deviation of 5. A sample of 100 observations will be taken. The probability that the mean from that sample will be between 49 and 51 is

a)0.50

b)0.6826

c)0.8413

d)0.9544

Answer 1

Solution :

Given that ,

mean = = 50

standard deviation = = 5

n = 100

= 50

=  / n=5 / 100=0.5

P(49<     <51 ) = P[(49-50) / 0.5< ( - ) /   < (51-50) /0.5 )]

= P( -2< Z <2 )

= P(Z <2 ) - P(Z <2 )

Using z table

=0.9772-0.0228

=0.9554

probability= 0.9554