Question 227729: Hello,
Would someone be able to help me with this statistics homework problem?
>Determine the following normal probabilities. Assume that, among residents of a large Florida subdivision, the population mean age is 65 years old, the population standard deviation is 2 years, and that the age variable is distributed normally.
1.What is the probability that a randomly chosen individual would be between 62 and 67 years of age? Draw a graph.
2.What is the probability that a randomly chosen individual would be less than 64 years of age?
3.What is the probability that a randomly chosen individual would be either less than 64 years of age or more than 66 years of age?
4.Find the specific age for which the following statement is true: The probability of being this age, or older, is 20%.
Thank you for your time,
Rob
Answer by stanbon(75887)   (Show Source):
You can put this solution on YOUR website! Determine the following normal probabilities. Assume that, among residents of a large Florida subdivision, the population mean age is 65 years old, the population standard deviation is 2 years, and that the age variable is distributed normally.
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You need to be able to find z-scores with a calculator or by
using a z-chart to work these problems.
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1.What is the probability that a randomly chosen individual would be between 62 and 67 years of age? Draw a graph.
z(62) = (62-65)/2 = -1.5
z(67) = (67-65)2 = 1
P(62 < x < 67) = P(-1.5 < z < 1) = 0.7745
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2.What is the probability that a randomly chosen individual would be less than 64 years of age?
z(64)= (64-65)/2 = -1/2
P(x < 64) = P(z < -1/2) = 0.3085
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3.What is the probability that a randomly chosen individual would be either less than 64 years of age or more than 66 years of age?
z(64) = -1/2
z(66) = (66-65)/2 = 1/2
P(x < 64 or x > 65) = P(z < -1/2 or x > 1/2 = P(z < -1/2) + P(z > 1/2)
= 0.3085 + 0.3085 = 0.6171
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4.Find the specific age for which the following statement is true: The probability of being this age, or older, is 20%.
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Find the z-value which has 20% of the population to the right:
That value is invNorm(0.80) = 0.8416
Now use x = zs +u to find the corresponding raw score.
x = 0.8416*2 + 65
x = 66.6832 (Prob of being this age or older is 20%)
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Cheers,
Stan H.
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