Question

A sample of size 105 will be drawn from a population with mean 15 and standard deviation 6 Use the Cumulative Normal Distribution Table if needed.

1) Find the probability that mean x will be greater than 16. Round the final answer to at least four decimal places.

2)Find the 55th percentile of x. Round the answer to at least two decimal places.

Answer 1

Solution :

Given that,

mean = = 15

standard deviation = = 6

n=105

= =15

= / n = 6 / 105 = 0.5855

P( > 16) = 1 - P( < 16)

= 1 - P[( - ) / < (16-15) /0.5855 ]

= 1 - P(z <1.71 )

Using z table

= 1 - 0.9564

= 0.0436

probability=0.0436

(B)  

Using standard normal table,

P(Z < z) = 55%

= P(Z < z) = 0.55  

= P(Z <0.13 ) = 0.55

z = 0.13 ( Using standard normal z table,)

Using z-score formula  

= z * +

= 0.13 * 0.5855+15

= 15.08