Question

Assume that on a standardized test of 100 questions, a person has a probability of 80% of answering any particular question correctly. Find the probability of answering between 76 and 86 questions, inclusive. (Assume independence, and round your answer to four decimal places.)

P(76 ≤ X ≤ 86) =

Answer 1

Solution :

Given that,

p = 0.80

q = 1 - p = 1 - 0.80 = 0.20

n = 100

Using binomial distribution,

Mean = = n * p = 100 * 0.80 = 80

Standard deviation = = n * p * q = 100 * 0.80 * 0.20 = 4

P(76   x 86)

= P[(76 - 80 /4 ) (x - ) / ( 86 - 80/ 4) ]

= P(-1.00 z 1.50)

= P(z 1.50) - P(z -1.00)

Using z table,  

= 0.9332 - 0.1587

= 0.7745