Question

A sample of size 35 will be drawn from a population with mean 43 and standard deviation 10.

a) is it appropriate to use normal distribution to find probability?

b) find the probability that x will be between 44 and 45. Round to at least 4 decimal places.

c) find the 37^th percentile of x. round to at least two decimal places.

Answer 1

Solution :

Given that ,

mean = = 43

standard deviation = = 10

n = 35

= 43

=  / n= 10 / 35=1.6903

P(44<     < 45) = P[(44-43) / 1.6903< ( - ) /   < (45-43) /1.6903 )]

= P( 0.59< Z < 1.18)

= P(Z <1.18 ) - P(Z <0.59 )

Using z table

=0.881-0.7224

=0.1586

probability= 0.1586

(B)

Using standard normal table,

P(Z < z) =37 %

= P(Z < z) = 0.37  

= P(Z <- 0.33 ) = 0.37

z =- 0.33 Using standard normal table,

Using z-score formula  

= z * +   

= - 0.33 *1.6903+43

= 42.44