What makes the normal distribution a probability distributio

What makes the normal distribution a probability distribution?

In a normal distribution, what percentage of the area under a normal curve is between µ - and µ + ?

In a normal distribution, what percentage of the area under a normal curve is between µ - and µ + 2?

Suppose you are interested in how long it takes to get your food at a restaurant. Now, suppose this distribution is approximately normal with an average of eight minutes and a standard deviation of two minutes. If you made a control chart for this data, what would be the highest control limit?

Using the above scenario, suppose someone gets the food after exactly eleven minutes. How many standard deviations from the mean is this value of eleven?

Using the above scenario, what is the probability that someone would get the food after more than eleven minutes?

Using the standard normal distribution, find the area below z=-0.8.

Using the standard normal distribution, find the area above z=-0.8.

Using the standard normal distribution, find the area between z=-0.8 and z=2.1.

Solution

X, a normal variable makes the distribution a prob distribution.

0.6826

0.9554

Highest control = 8+3 sigma = 14

x=11 means z = 3/2 = 1.5

P(X>11) = P(X>1.5) = 0.5-0.4332

= 0.0668

Std dev = 1.5 from mean

More than 11 also same prob

Using the standard normal distribution, find the area below z=-0.8.   Area = 0.2119

Using the standard normal distribution, find the area above z=-0.8.   Area = 0.7881

Using the standard normal distribution, find the area between z=-0.8 and z=2.1 Area = 0.2881+0.4821= 0.7702