Question

If 15% of adults in a certain country work from home, what is the probability that fewer than 42 out of a random sample of 350 adults will work from home? (Round your answer to 3 decimal places)

Thank you very much please give me an exact answer with the explanation!

Answer 1

Answer)

First we need to check the conditions of normality that if n*p and n*(1-p) both are greater than 5 or not

N = 350

P = 42/350

N*(1-p) = 308

N*p = 42

As both are greater than, 5

Normality conditions are met, so we can use standard normal z table to estimate the probability

We need to find mean

P = 0.15

Mean = 350*0.15 = 52.5

Standard deviation = √n*p*(1-p)

= 6.6801946079436

Z = (x-mean)/s.d

And by uncertainty

P(x<42) = p(x<41.5)

Z = (41.5 - 52.5)/6.6801946079436 = -1.65

From z table

P(z<-1.65) = 0.0495