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) please explain in ti-84 terms

Answer 1

Solution:

We are given

n = 350

p = 0.15

q = 1 – p = 1 – 0.15 = 0.85

np = 350*0.15 = 52.5 > 5

nq = 350*0.85 = 297.5 > 5

np > 5 and nq > 5

So, we can use normal approximation to binomial distribution.

We have

Mean = np = 350*0.15 = 52.5

SD = sqrt(npq) = sqrt(350*0.15*0.85) = 6.680195

We have to find P(X<42)

P(X<42) = P(X<41.5) (by using continuity correction)

Z = (X – mean) / SD

Z = (41.5 - 52.5) / 6.680195

Z = -1.64666

P(Z<-1.64666) = P(X<42) = 0.049814

(by using z-table)

Required probability = 0.050

Ti-84 steps:

Start calculator

Press DISTR (2^nd VARS)

Select #2: normalcdf function

Enter lower bound = -1E99

Enter upper bound = 41.5

Enter mean = 52.5

Enter standard deviation = 6.680195

ENTER

You will get required probability.