In a study by Peter D. Hart Research Associates for the Nasdaq Stock Market, it
ID: 1157566 • Letter: I
Question
In a study by Peter D. Hart Research Associates for the Nasdaq Stock Market, it was determined that 20% of all stock investors are retired people. In addition, 40% of all adults invest in mutual funds. Suppose a random sample of 25 stock investors is taken.
*Round your answer to 3 decimal places.
e. Suppose a random sample of 20 adults is taken. What is the probability that fewer than six adults invested in mutual funds?
P(x < 6) =
*
f. Suppose a random sample of 20 adults is taken. What is the probability that exactly one adult invested in mutual funds?
P(x = 1) =
*
g. Suppose a random sample of 20 adults is taken. What is the probability that 13 or more adults invested in mutual funds?
P(x ? 13) =
*
h. For parts e–g, what exact number of adults would produce the highest probability? How does this compare to the expected number?
x =
Expected Number = µ =
Explanation / Answer
Ans for e)
P(x<6)=P(X=0)+P(X=1)+P(X=2)+P(X=3)+P(X=4)+P(X=5)
P(X=0)=20C0*0.4^(0)*).6^20=6^20=0.000036
P(X=1)=20C1*0.4*).6^19=20*0.4*0.6^19=0.000487
P(X=2)=20C2*0.4^2*0.6^18=380**0.4^2*0.6^18=0.0002627
P(X=3)=20C3*0.4^3*0.6^17=1140*0.4^3*0.6^17=0.01234
P(X=4) =20C4*).4^4*0.6^16=4845*0.4^4*0.6^16=0.03499
P(X=5)=20C5*0.4^5*0.6^15=15504*0.4^5*0.6^15=0.07467
P(X<6)=0.1227
Ans f)
P(X=1)=20C1*0.4*.6^19=20*0.4*0.6^19=0.000487
Ans g)
P(X>=13)=1-P(X<7)=1-P(X=7)-P(X=6)-P(X<=5)
=1-20C7*0.4^7*).6^13-20C6*0.4^6*0.6^14-P(X<=5)
=1-77520*0.4^7*0.6^13-38760*0.4^6*0.6^14-0.1227
P(X>=13)=0.5870
Ans h
Expected number =n*p*(1-p)=20*0.4*0.6=4.8