Question

Scores of adults aged 60 to 64 on a common IQ test are approximately Normally distributed with mean 90 and standard deviation 15

1. Since IQ scores of adults aged 60 to 64 are Normally distributed with mean 90 and sd 15, then about 40% of the scores are between

a. 60 and 120

b. 45 and 135

c. 85 and 90

d. the 25th and 75th percentile

e. the 30th and 70th percentile

2. What range of IQ scores contains th ecentral 95% of the population of adults aged 60 to 64?

a. 75 to 105

b. 60 to 120

c. 30 to 150

d. 45 to 135

3. The third quartile of the distribution of IQ scores of adults aged 60 to 64 is between

a. 90 to 105

b. 90 to 75

c. 105 to 120

d. 60 to 75

4. Suppose we call an IQ of 90 "normal" for adults aged 60 to 64. What percent of the population have "below normal" IQs?

a. about 50%

b. less than 50%

c. More than 50%

d. Cant tell from the information given.

Answer 1

Q 1 ) X ~N(90, 15)

The 40% of score lies between 30th and 70th percentile . It also lies between 25th and 75th percentile but the minimum range is 30th and 70th percentile

Answer: Option e) the 30th and 70th percentile

Q 2) Range of IQ scores contains 95% Confidence is

Solution : The critical value of Z for 95% CI is +/-2 (using empirical rule )

Therefore the lower bound is

The upper bound is

Answer: Option b. 60 to 120

Q 3) The Z value for third quartile is 0.674

Therefore the third quartile is

Hence it is lie between 90 to 105

Answer: Option a) 90 to 105

Q 4) Answer: a. about 50%

Because IQ scores follows normal distribution and the mean score is 90. the area below the mean is 50%