Question

Suppose that a new treatment is successful in curing a common ailment 71% of the time. If the treatment is tried on a random sample of 140 patients, approximate the probability that at least 101 will be cured. Use the normal approximation to the binomial with a correction for continuity. Round your answer to at least three decimal places. Do not round any intermediate steps.

Answer 1

Solution :

Given that,

p = 0.71

q = 1 - p =1 - 0.71=0.29

n = 140

Using binomial distribution,

= n * p = 140 *0.71=99.4

= n * p * q = 140*0.71*0.29=5.3690

Using continuity correction ,

P(x > 100.5) = 1 - P(x <10.5 )

= 1 - P((x - ) / < (100.5 - 99.4) / 5.3690)

= 1 - P(z <0.20 )

= 1 -0.5793

=0.4207

answer =0.421