(a) Given a random varniable X which is normally distributed with mean 15 and standard deviation 10, find: i. P(X< 20) ii. P(X>12) ii. P(12

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1. (a) Given a random variable X which is normally distributed with mean 15 and
standard deviation 10, find:
i. P(X< 20)
ii. P(X>12)
iii. P(12 <X< 20)
b. Solve the equations simultaneously using Cramer's Rule
x - 2y - 3z = 0
3x + 5y + 2z =0
2x + 3y - z = 2
2. Two in 10 marketing strategies randomly sampled are known to be ineffective in a
banking sector.
a. Calculate the probability that in a sample of 6 marketing strategies employed
in the banking sector:
i. None are ineffective
ii. More than half are ineffective
b. Find the:
i. Expected number of ineffective strategies, and
ii. Standard deviation of ineffective strategies used in the banking sector.
3. A stock market analysis claims that the average annual retum in the Aviation sector is
12%. The Business consultant want to test whether this claim is true. The Business
consultant collected a random sample of 36 stocks in the Aviation sector and that the
average annual return is 10% with a standard deviation of 3%. Use a 5% level of
significance to test the analyst's claim.
Transcribed Image Text:1. (a) Given a random variable X which is normally distributed with mean 15 and standard deviation 10, find: i. P(X< 20) ii. P(X>12) iii. P(12 <X< 20) b. Solve the equations simultaneously using Cramer's Rule x - 2y - 3z = 0 3x + 5y + 2z =0 2x + 3y - z = 2 2. Two in 10 marketing strategies randomly sampled are known to be ineffective in a banking sector. a. Calculate the probability that in a sample of 6 marketing strategies employed in the banking sector: i. None are ineffective ii. More than half are ineffective b. Find the: i. Expected number of ineffective strategies, and ii. Standard deviation of ineffective strategies used in the banking sector. 3. A stock market analysis claims that the average annual retum in the Aviation sector is 12%. The Business consultant want to test whether this claim is true. The Business consultant collected a random sample of 36 stocks in the Aviation sector and that the average annual return is 10% with a standard deviation of 3%. Use a 5% level of significance to test the analyst's claim.
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