A European growth mutual fund specializes in stocks from the British Isles, cont

Question

A European growth mutual fund specializes in stocks from the British Isles, continental Europe, and Scandinavia. The fund has over 300 stocks. Let x be a random variable that represents the monthly percentage return for this fund. Suppose x has mean = 1.3% and standard deviation = 1.4%.

After 9 months, what is the probability that the average monthly percentage return x will be between 1% and 2%? (Round your answer to four decimal places.)


(c) After 18 months, what is the probability that the average monthly percentage return x will be between 1% and 2%? (Round your answer to four decimal places.)

If after 18 months the average monthly percentage return x is more than 2%, would that tend to shake your confidence in the statement that = 1.3%? If this happened, do you think the European stock market might be heating up? (Round your answer to four decimal places.)
P(x > 2%) =

Explanation / Answer

mean = 1.3, s = 1.4
b)

n =9
P(1 < x < 2)
= P(( x - mean ) /(s/sqrt(n)) <z < ( x - mean ) /(s/sqrt(n))
= P ((1 - 1.3) / ( 1.4 /sqrt(9)) < z < (2 - 1.3) / ( 1.4 /sqrt(9))
= P(0.6428 < z < 1.5)

P(1 < x < 2) = P(0.6428 < z < 1.5) = 0.673

c)

n = 18
P(1 < x < 2)
= P(( x - mean ) /(s/sqrt(n)) <z < ( x - mean ) /(s/sqrt(n))
= P ((1 - 1.3) / ( 1.4 /sqrt(18)) < z < (2 - 1.3) / ( 1.4 /sqrt(18))
= P(0.9091 < z < 2.121)

P(1 < x < 2) = P(0.6428 < z < 1.5) = 0.8015

d)
P(x > 2%)
z = ( x - mean) / ( s/sqrt(n))
= (2 - 1.3) / ( 1.4 /sqrt(18))
= 2.121
P(X > 2) = p(Z > 2.121) = 0.0169

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