Question

Surgical face masks coming off an assembly line can either be declared defective or nondefective. Suppose that 40 percent of the masks are defective. If 200 masks are randomly selected what is the approximate probability (in a large sample sense) that at most 45 of the masks will be defective?

Answer 1

Solution:

Given ,

p = 40% = 0.40 (population proportion)

n = 200 (sample size)

Let be the sample proportion.

The sampling distribution of is approximately normal with

mean = =  p = 0.40

SD =   =     

=  \sqrt{0.40(1-0.40)/200}

=  0.03464101615

Now ,

P( at most 45 of the masks will be defective)

= P( 45/200)

= P(   0.225)

=

=  P(Z <(0.225 -0.40)/0.03464101615 )

= P(Z < -5.05)

= 0.0000 ...use z table