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 1% of these tests end in failure?

Select one:

a. 0.0588

b. 0.9412

c. 0.9706

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

e. 0.0294

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 ] = 0.0052915

P( <0.01 ) =

= P[( - ) / < (0.01 -0.02) /0.0052915 ]

= P(z <-1.89 )

Using z table,   

=0.0294

probability=0.0294