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Old 07-28-2007   #1
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Default Probability/Stats Questions?

Can someone please help me solve the following questions?Scores on a test are normally distributed with a mean of 550 and a standard deviation of 80. a) If one subject is randomly selected, find the probability that the score is between 550 and 650. b) If a job requires a score in the top 80%, find the lowest acceptable score. C) If 50 subjects are randomly selected, find the probability that their mean is between 550 and 650.Thanks!!!
Old 07-28-2007   #2
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How's it going.a) the dif. between 650and 550 is 100. a standard dev. = 80.so we will have 34% + 13.5(.25)%= 3.375 + 34= 37.375%answer to a is 37.375%b)idkc)37.375%*50= 18.675=19 people
Old 07-28-2007   #3
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a) To find the probability of a variable, X, between two limits, a and b when the variable is normally distributed:P(a < X < b) = Φ[(b-µ)/σ] - Φ[(a-µ)/σ] where the values within the square brackets are standard normal z-values. Phi (Φ) is and operator that means "find the probability associated with the Z-values in the square brackets". So evaluating:P(550 < X < 650) = Φ[(650-550)/80] - Φ[(550-550)/80] P(550 < X < 650) = Φ[(650-550)/80] = Φ[1.25] - Φ[0] = 0.8944 - 0.50 = 0.3944b) You want to eliminate the bottom 20%. So the Z-value associated with the BOTTOM 20% is -0.84, and the limit for the bottom 20% is found by:-0.84 = (x - 550)/80; solving for x = 482.8. If an integer is required, then the lowest acceptable score would be 483.c) Find the probability that the sample mean is less than 650:Z = (650-550)/(80/√50) = 100/35.78) = 2.79Then Φ[2.79] - Φ[0] = 0.9974 -0.50 = 0.4974

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