Question

Below, n is the sample size, p is the population proportion of successes, and X is the number of successes in the sample. Use the normal approximation and the TI-84 Plus calculator to find the probability. Round the answer to at least four decimal places.

n=76, p=0.41

P(28<X<38)=

Answer 1

Solution:

Given that,

p = 0.41

1 - p = 1 - 0.41 = 0.59

n = 76

Here, BIN (76 ,0.41 )

then,

n*p = 76 * 0.41 = 31.16

n(1- p) = 44.84

Since both are greater than 5 , we can use normal approximation to binomial.

According to normal approximation binomial,

X Normal

Mean = = n*p = 31.16

Standard deviation = =n*p*(1-p) = [76*0.41*0.59] = 4.28770334795

Find P(28<X<38) using TI-84 Plus calculator

Press 2nd and then press VARS

Go to normalcdf(

normalcdf(lower , upper , ,

normalcdf(28 , 38  , 31.16  , 4.28770334795

= 0.7141

Answer : 0.7141