5.3

1. A distribution of values is normal with a mean of 1493.5 and a standard deviation of 45.7

Find the probability that a randomly selected value is less than 1528.7

P (X < 1528.7) = _________________

*Enter your answer as a number accurate to 4 decimal places. * Note all z-scores must be rounded to the nearest hundredth*

2. A distribution of values is normal with a mean of 822.2 and a standard deviation of 45.1

Find the probability that a randomly selected value is greater than 935.4

P (X > 935.4) = ________________

*Enter your answer as a number accurate to 4 decimal places. * Note all z-scores must be rounded to the nearest hundredth*

3. A distribution of values is normal with a mean of 684.5 and a standard deviation of 27.5

Find the probability that a randomly selected value is between 643.8 and 700.2

P (643.8 < X < 700.2) = ______________

*Enter your answer as a number accurate to 4 decimal places. * Note all z-scores must be rounded to the nearest hundredth*

4. The number of miles a certain type of brake pad will last is normally distributed with a mean of 56000 miles and standard deviation 2590 miles. Find the probability that, if you install this type of brake pad, it will last more than 59315 miles.

P(X> 59315) = _________________

*Enter your answer as a number accurate to 4 decimal places. * Note all z-scores must be rounded to the nearest hundredth*

5. The heights of women aged 20-29 are normally distributed with mean 65.7 inches and standard deviation 3.3 inches. What percent of women are below 59.7 inches? Round to the nearest hundredth of a percent? _________________

*Enter your answer as a percent rounded to the nearest hundredth*Note: all z-scores must be rounded to the nearest hundredth*

6. Statista reported in 2014 that the mean number of Facebook friend for 18 to 24-year old’s was 649. Assuming the distribution is normal with mean 649 friends and standard deviation 120 friends, what is the probability that a randomly selected 18 to 24-year-old will have between 435 and 985 friends?

P (435< X < 985) = _______________

*Enter your answer as a number accurate to 4 decimal places. *Note: all z-scores must be rounded to the nearest hundredth*

7. Suppose that a brand of lightbulb lasts on average 2628 hours with a standard deviation of 138 hours. Assume the life of the lightbulb is normally distributed. Calculate the probability that a particular bulb will last from 2191 to 3064 hours?

P (2191< X <3064) = _____________

*Enter your answer as a number accurate to 4 decimal places. * Note all z-scores must be rounded to the nearest hundredth*

8. Suppose a drive for a PGA Tour golfer is 316.93 yards with a standard deviation of 16.5 yards. Find the probability that a random drive will travel more than 317.9 yards.

P(X> 317.9) = _____________

*Enter your answer as a number accurate to 4 decimal places. *Note: all z-scores must be rounded to the nearest hundredth*

9. Assume that the readings at freezing on a batch of thermometers are normally distributed with a mean of 0 degree Celsius and a standard deviation of 1.00 degree Celsius.

A single thermometer is randomly selected and tested. Let X represent the reading of this thermometer at freezing. What reading separates the highest 33.36% from the rest? 

c= ______ degree Celsius