1. Suppose a brewery has a filling machine that fills 12 ounce bottles of beer. It is known that the amount of beer poured by this filling machine follows a normal distribution with a mean of 12.27 ounces and a standard deviation of 0.06 ounce. Find the probability that the bottle contains between 12.17 and 12.23 ounces

2. Assume that heights of men
are normally distributed, with a mean of 68.9 in . and a standard deviation of 2.8 in. If 68 men are randomly selected, Find the probability that they have have heights with a mean greater than 68.5

3. suppose x is a uniform variable with a=1 and b=20. find the standard deviation

4. Assume that blood pressure readings are normally distributed with a mean of 124 and a standard deviation of 6.4 . If 25 people are randomly selected, find the probability that their mean blood pressure will be less than 126.

5. The lengths of pregnancies are normally distributed with a mean of 273 days and a standard deviation of 30 days. If 144 women are selected, Find the probability that they have a mean pregnancy between 273 and 275 days.

6. The diameter of ball bearings produced in a manufacturing process can be explained using a uniform distribution over the interval 8.5 to 10.5 mm. what is the probability that a randomly selected ball bearing has a diameter less than 9.1 mm?