Question

Suppose that 6.5% of all persons are allergic to penicillin. A sample of 561 persons is selected.

a. the probability that less than 8% of persons in the sample will be allergic to penicillin is approximately?

b. the probability then 7.5% to 9% of persons in the sample will be allergic to penicillin is approximately?

Answer 1

Solution :

Given that ,

p = 0.065

1 - p = 0.935

n = 561

= p = 0.065

= (p*(1-p))/n =  (0.065*0.935)/ 561= 0.01040

a)

P( <0.08 ) = P(( - ) / < (0.08 - 0.065) / 0.01040)

= P(z < 1.442)

= 0.9253

The probability that less than 8% of persons in the sample will be allergic to penicillin is approximately 0.9253

b)

P(0.075 < <0.09 ) = P((0.075-0.065)/0.01040 ) < ( - ) /  < (0.09-0.065) /0.01040 ) )

= P(0.962 < z < 2.404 )

= P(z < 2.404) - P(z < 0.962)

= 0.9919 - 0.8320

= 0.1599

The probability then 7.5% to 9% of persons in the sample will be allergic to penicillin is approximately 0.1599