Question

A random sample of size 36 is taken from a population with mean µ = 17 and standard deviation σ = 4. The probability that the sample mean is greater than 18 is ________.

a. 0.8413

b. 0.0668

c. 0.1587

d. 0.9332

Answer 1

Solution :

Given that ,

mean = = 17

standard deviation = = 4

n = 36

= 17

= / n =4 / 36 = 0.6667

P( >18 ) = 1 - P( < 18)

= 1 - P[( - ) / < (18-17) / 0.6667]

= 1 - P(z <1.50 )

Using z table

= 1 - 0.9332

= 0.0668

probability= 0.0668