## Use the normal distribution of IQ​ scores

9. Use the normal distribution of IQ​ scores, which has a mean of 110 and a standard deviation of 15​, and the following table with the standard scores and percentiles for a normal distribution to find the indicated quantity.

Percentage of scores less than 140 is____​%.

10. Use the normal distribution of IQ​ scores, which has a mean of 110 and a standard deviation of 18 ​, and the following table with the standard scores and percentiles for a normal distribution to find the indicated quantity.

Percentage of scores less than 146 is enter your response here­­­­____%. (Round to two decimal places as​ needed.)

11. Use the normal distribution of IQ​ scores, which has a mean of 90 and a standard deviation of 15​, and the following table with the standard scores and percentiles for a normal distribution to find the indicated quantity.

Percentage of scores greater than 120 is___​%. (Round to two decimal places as​ needed.)

12. Use the normal distribution of IQ​ scores, which has a mean of 130 and a standard deviation of 16 ,and the following table with the standard scores and percentiles for a normal distribution to find the indicated quantity.

The percentage of scores between 114 and 146 Is___​%. (Round to two decimal places as​ needed.)

13. Use the normal distribution of IQ​ scores, which has a mean of 75 and a standard deviation of 12​, and the following table with the standard scores and percentiles for a normal distribution to find the indicated quantity.

The percentage of scores between 63 and 99 Is___​%. (Round to two decimal places as​ needed.)

14. Use the normal distribution of heights of adult​ women, which has a mean of 164 centimeters and a standard deviation of 6 centimeters and the following table with the standard scores and percentiles for a normal distribution to find the indicated quantity.

The percentage of heights greater than 158 centimeters is___%.(Round to two decimal places as​ needed.)

15. Use the normal distribution of heights of adult​ women, which has a mean of 163 centimeters and a standard deviation of 9 centimeters, and the following table with the standard scores and percentiles for a normal distribution to find the indicated quantity.

The percentage of heights less than 158.5 centimeters is__​%. (Round to two decimal places as​ needed.)

17. Rolling a fair twelve-sided die produces a uniformly distributed set of numbers between 1 and 12 with a mean of 6.5 and a standard deviation of 3.452. Assume that n twelve-sided dice are rolled many times and the mean of the n outcomes is computed each time.

a. Find the mean and standard deviation of the resulting distribution of sample means for n=___

The mean of the resulting distribution of sample means is___

​(Round to the nearest tenth as​ needed.)

The standard deviation of the distribution of sample means is___

​(Round to the nearest thousandth as​ needed.)

b. Find the mean and standard deviation of the resulting distribution of sample means for n=___

The mean of the resulting distribution of sample means is___

​(Round to the nearest tenth as​ needed.)

The standard deviation of the distribution of sample means is___

​(Round to the nearest thousandth as​ needed.)

18. A safety light is designed so that the times between flashes are normally distributed with a mean of 4.50 s and a standard deviation of 0.70 s.

a. Find the probability that an individual time is greater than 5.50 s.

b. Find the probability that the mean for 60 randomly selected times is greater than 5.50 s.

c. Given that the light is intended to help people see an​ obstruction, which result is more relevant for assessing the safety of the​ light?

Part 1

a. The probability is approximately____. (Round to four decimal places as​ needed.)

b. The probability is approximately____. (Round to four decimal places as​ needed.)

19. Researchers for a manufacturer of barometers​ (devices to measure atmospheric​ pressure) read each of 50 barometers at the same time of day. The mean of the readings is 30.3 (inches of​ mercury) with a standard deviation of 0.26 inch, and the readings appear to be normally distributed.

a. What percentage of the barometers read over 30.95?___​%  (Round to two decimal places as​ needed.)

b. What percentage of the barometers read less than 29.65​?___​% (Round to two decimal places as​ needed.)

c. The company decides to reject barometers that read more than 2 standard deviations above or below the mean. What is the critical reading below which barometers will be​ rejected? ___ (Round to two decimal places as​ needed.)

What is the critical reading above which barometers will be​ rejected? ____ (Round to two decimal places as​ needed.)

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