In a large population of collegeeducated adults the mean IQ

In a large population of college-educated adults, the mean IQ is 115 with a standard deviation of 20. Suppose 100 adults from this population are randomly selected for a market research campaign. The parameter(s) here is(are) the mean IQ (mu) of college educated adults. the standard deviation (sigma) of IQs. of college educated adults. Neither A nor B Both A and B A statistic here is the mean IQ (mu) of college educated adults. the standard deviation (sigma) of IQs of college educated adults. the sample mean IQ x calculated from the 100 college-educated adults. None of the above The distribution of the sample mean IQ is exactly Normal, mean 115, standard deviation 20. approximately Normal, mean 115, standard deviation 0.2. approximately Normal, mean 115, standard deviation 2. approximately Normal, mean equal to the observed sample mean value, standard deviation 20. The probability that the sample mean IQ is between 110 and 120 is 0.0062. 0.9876. 0.9938. 0.9207

Solution

Parameters are for populations, and statistics are for samples.

a)

D. BOTH A AND B.

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b)

C. the sample mean IQ xbar calculated from the 100 college-educated adults [ANSWER]

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c)

By central limit theorem,

OPTION C: approx Normal, mean 115, standard deviation 2. [ANSWER]

This is because the mean stays the same, and the standard deviation gets divided by sqrt(n), and n = 100 here.

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d)

We first get the z score for the two values. As z = (x - u) sqrt(n) / s, then as          
x1 = lower bound =    110      
x2 = upper bound =    120      
u = mean =    115      
n = sample size =    100      
s = standard deviation =    20      
          
Thus, the two z scores are          
          
z1 = lower z score = (x1 - u) * sqrt(n) / s =    -2.5      
z2 = upper z score = (x2 - u) * sqrt(n) / s =    2.5      
          
Using table/technology, the left tailed areas between these z scores is          
          
P(z < z1) =    0.006209665      
P(z < z2) =    0.993790335      
          
Thus, the area between them, by subtracting these areas, is          
          
P(z1 < z < z2) =    0.987580669 = 0.9876 [ANSWER, B]