A company is going to release four quarterly reports this year. Suppose the comp

Question

A company is going to release four quarterly reports this year. Suppose the company has a 32% chance of beating analyst expectations each quarter. (10 pts)

a). What is the probability that the company beats analyst expectations every quarter of this year?

b). What is the probability the company beats analyst expectations more than half the time this year?

c). What is the expected number of times the company will beat analyst expectations this year? How much is this expected to vary?

d). What is the probability the company will not beat analyst expectations for exactly two quarters?

Explanation / Answer

This account sfor binomial distribution with probability of success, p=0.32, the total number of tials, n=4 and specific number of successes in n trials is denoted by r. Use P(X,r)=nCr(p)^r(q)^n-r.

a) P(X=4)=4C4(0.32)^4(0.68)^4-4=0.0105

b) P(X>2)=1-P(X<=2)=1-[P(X=0)+P(X=1)+P(X=2)]=1-[0.4624+0.4352+0.1024]=0.0000

c) E(X)=np=4*0.32=1.28

d)P(X=2)=4C2(0.32)^2(0.68)^4-2=0.2849

Hope this will helpful to you :)

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