Question

A sample of size 34 will be drawn from a population with mean 44 and standard deviation 9.

(a) Is it appropriate to use the normal distribution to find probabilities for x?
(b) If appropriate find the probability that x will be between 45 and 46. Round the answer to at least four decimal places.
(c) If appropriate find the 38th percentile of mean=x Round the answer to at least two decimal places.

Answer 1

Solution :

Given that,

mean = = 44

standard deviation = = 9

a) n = 34

= = 44

= / n = 9 / 34 = 1.54

b) P(45 < < 46 )  

= P[(45 - 44) / 1.54 < ( - ) / < (46 - 44) / 1.54)]

= P( 0.65 < Z < 1.30)

= P(Z < 1.30) - P(Z < 0.65)

Using z table,  

= 0.9032 - 0.7422

= 0.1610

Given that,

c) Using standard normal table,

P(Z < z) = 38%

= P(Z < z ) = 0.38

= P(Z < z ) = 0.38  

z = - 0.31

Using z-score formula  

= z * +   

= - 0.31 * 1.54 + 44

= 43.52