Question

A population has a mean of 50 and a standard deviation of 8. A sample of 64 observations will be taken. The probability that the mean from that sample will be larger than 49 is

a)0.1587

b)0.8413

c)0.0228

d)0.9772

Answer 1

Solution :

Given that ,

mean = = 50

standard deviation = = 8

n = 64

= 50

= / n = 8 / 64= 1

P( > 49) = 1 - P( < 49)

= 1 - P[( - ) / < (49 -50) / 1]

= 1 - P(z <-1 )

Using z table

= 1 - 0.1587

= 0.8413

probability= 0.8413