Question 347582: 1-the graduate selection committee wants to select the top 10% of applicants. On a standardized test with a mean of 500 and a standard diviation of 100, what would be the cutoff score for selecting the top 10% of applicants, assuming that test is normally distributed?
2- The average commute time via train from the chicago O'Hare Airport to downtown is 60 minutes with a s=15 minutes.Assume that the commute times are normally distributed. what proportion of communtes would be:
a. Longer than 80 minutes?
b. Less than 50 minutes?
c. Between 45 and 75 minutes?
3- Bob takes an online IQ test and finds out that his IQ according to the test is 134. Assuming that the mean IQ is 100, the s=15, and the distribution of IQ scoes is normal, what proportion of the population would score higher than Bob? Lower than Bob?
Answer by stanbon(75887)   (Show Source):
You can put this solution on YOUR website! 1-the graduate selection committee wants to select the top 10% of applicants. On a standardized test with a mean of 500 and a standard diviation of 100, what would be the cutoff score for selecting the top 10% of applicants, assuming that test is normally distributed?
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Find the z-value with a right tail of 10%: invNorm(0.90) = 1.2816
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Then use x = zs+u to find the raw score (x).
x = 1.2816*100+500 = 628.16
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2- The average commute time via train from the chicago O'Hare Airport to downtown is 60 minutes with a s=15 minutes.Assume that the commute times are normally distributed. what proportion of commutes would be:
a. Longer than 80 minutes?
z(80) = (80-60)/15 = 4/3
P(x> 80) = P(z> 4/3) = normalcdf(4/3,100) = 0.0912
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b. Less than 50 minutes?
z(50) = (50-60)/15 = -2/3
P(x< 50) = P(z< -2/3) = normalcdf(-100,-2/3) = 0.2525
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c. Between 45 and 75 minutes?
Same procedure.
Can you do that?
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3- Bob takes an online IQ test and finds out that his IQ according to the test is 134. Assuming that the mean IQ is 100, the s=15, and the distribution of IQ scoes is normal, what proportion of the population would score higher than Bob? Lower than Bob?
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Find z-score of 134 = N.
Find P(z >N)
Find P(z < N)
Can you do that?
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Cheers,
Stan H.
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