Question

Consider the probability that greater than 96 out of 145 people will not get the flu this winter. Assume the probability that a given person will not get the flu this winter is 61%. Approximate the probability using the normal distribution. Round your answer to four decimal places.

Answer 1

Solution

Given that,

p = 61% = 0.61

1 - p = 1 - 0.61 = 0.39

n = 145

= p = 0.61

=  [p( 1 - p ) / n] = [(0.61 * 0.39 ) / 145 ] = 0.0405

X = 96

= x / n = 96 / 145 = 0.66

P( > 0.66 ) = 1 - P( < 0.66 )

= 1 - P(( - ) / < ( 0.66 - 0.61 ) / 0.0405 )

= 1 - P(z < 1.23 )

Using z table

= 1 - 0.8907

= 0.1093