According to the CICA Business Monitor, 11% of Canada\'s executive chartered acc

Question

According to the CICA Business Monitor, 11% of Canada's executive chartered accountants are pessimistic about the economy. To check this claim, 48 chartered accountants were randomly selected and asked whether they feel pessimistic about the economy in 2013.

(a) If the claim is true, find the probability (±0.0001) that exactly seven chartered accountants are pessimistic about the economy. P(X=7) =

(b) If the claim is true, find the probability (±0.0001) that at most five chartered accountants are pessimistic about the economy P(X5) =

(c) Suppose 12 chartered accountants are pessimistic about the economy. P(X12) (±0.0001) = ? Conclusion: There is no evidence to suggest the claim is false or There is evidence to suggest the claim is false

Explanation / Answer

here p=0.11, n=48, since n is >30, we approximate this to normal distirbution.

mean=np=5.28

sd=sqrt(npq)=2.1677

a) P(X=7)=P(6.5<x<7.5)

using NORMDIST function in excel for 6.5 and 7.5, we subtract the two values [NORMDIST(7.5,5.28,2.1677,TRUE)]

=0.84711-0.7132=0.13391

b) PX<=5)=P(X<=5.5)=NORMDIST(5.5,5.28,2.1677,TRUE)=0.5404

c) P(X>=12)=P(X>=12.5)=1-P(X<=12.5)=1-NORMDIST(12.5,5.28,2.1677,TRUE)=1-0.99956=0.00043

The above proabability is too samll, hence there is no evidence to suggest the claim is false.

Related Questions

Navigate

• Browse (All)
• Browse A
• Subjects

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.