Question

A sample of size 75 will be drawn from a population with mean 35 and standard deviation 10.Use the Cumulative Normal Distribution Table if needed.

1) Find the probability that mean=x will be greater than 32. Round the final answer to at least four decimal places.

2) Find the 65th percentile of mean=x. Round the answer to at least two decimal places.

Answer 1

Solution :

Given that ,

mean = = 35

standard deviation = = 10

n = 75

= 35

= / n = 10 / 75 = 1.15

P( > 32) = 1 - P( <32 )

= 1 - P[( - ) / < (32-35) /1.15 ]

= 1 - P(z < -2.61)

Using z table

= 1 - 0.0045

= 0.9955

probability= 0.9955

2.

Using standard normal table,

P(Z < z) = 65%

= P(Z < z) = 0.65  

= P(Z <0.39 ) = 0.65

z = 0.39 Using standard normal table,

Using z-score formula  

= z * +   

= 0.39*1.15+35

= 35.45