Probability homework question

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A testing program requires applicants to take an IQ test to determine eligibility for the scholarship. IQ scores are normally distributed with a mu (mean) of 100 and a standard deviation (lowercase sigma) of 15. Using these data answer the following questions.
a. If a college admission office requires scores of at least the 84th percentile for admission, what is the cutoff score?

b. What is the probability of randomly selecting a “test taker” with a score
1) Greater than or equal 140?
2) Less than or equal 70?
3) Between 94 and 106?

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@mihanni21 ,

Use the standard normal distribution--note the total area under the curve is 1

modify this to a mean of 100 and a sigma of 15.

>140 P(e)=0.383%
Use an online calculator or a standard normal distribution table and calculate the probability of less than 140 and subtract this from 1 for the greater number.

<70 P(e)=2.275%
easier use <70 directly

between 94 and 106 P(e)=31.085%
<94 has P(e)= 34.458%
<106 has P(e)= 65.543%
P(106)-P(94)=65.543-34.458

Rap

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@raprap,

Thank you! How do I answer part a) of this question??

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@mihanni21 ,

Again use the standard normal distribution with the same mean and sigma. You're looking for a score that is greater than 84% of he population

(P(e)=1-.84=0.16)

You already know from b that 140 is more than enough (0.3%) and 104 is too low (65%) so start with something between 104 and 140--say 120 and try it.

I get 91% for 120 & 84% for 115 (1 standard deviation)

Rap

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Probability homework question

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