**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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