Question

A certain statistical test is designed so that it fails 2% of the time. Suppose that 700 of these tests are randomly selected, and we wish to calculate the proportion of these tests that result in a failure. What is the probability that less than 2.5% of these tests end in failure?

Select one:

a. 0.0000

b. 0.8264

c. 0.6528

d. We cannot reliably calculate this probability with the information given.

e. 0.1736

f. 0.3472

Answer 1

Solution

Given that,

p = 0.02

1 - p = 1 -0.02=0.98

n = 700

= p =0.02

=  [p ( 1 - p ) / n] =   [(0.02*0.98) /700 ] = 0.005292

P( < 0.025) =

= P[( - ) / < (0.025 -0.02) / 0.005292]

= P(z <0.94 )

Using z table,

=0.8264

probability=0.8264