Finding Areas within a Normal Distribution Answers

In a standard Normal distribution, what percentage of observations lie above z = 1.65?Find the z-table here.

Keeping car tires inflated is essential to safe driving. For one type of car tire, the tire pressure in pounds per square inch (psi) is assumed to be approximately Normal, with a mean of 35 psi and a standard deviation of 2 psi. What percentage of tires are inflated to a pressure above 36 psi?Find the z-table here.

The daily high temperatures in a vacation resort city are approximately Normal, with a mean temperature of 75 degrees Fahrenheit and a standard deviation of 6 degrees. What percentage of days have a high temperature below 77 degrees?Find the z-table here.

Many states have fishing regulations that require anglers to throw back caught fish if they do not meet length requirements. For the red drum species, a caught fish must be thrown back if it is not between 21 and 28 inches long. The lengths of the red drum species of fish have an approximately Normal distribution, with a mean length of 24 inches and a standard deviation of 1.4 inches. What proportion of red drum fish must be thrown back?Find the z-table here.

In a standard Normal distribution, what percentage of observations lie between z = 0.37 and z = 1.65?Find the z-table here.

The lifespans of crocodiles have an approximately Normal distribution, with a mean of 18 years and a standard deviation of 2.6 years. What proportion of crocodiles live less than 14 years?Find the z-table here.

The lengths of the red drum species of fish are approximately Normally distributed, with a mean length of 24 inches and a standard deviation of 1.4 inches. What proportion of red drum fish are less than 23 inches in length?Find the z-table here.

A machine at a food-distribution factory fills boxes of rice. The distribution of the weights of filled boxes of rice has an approximately Normal distribution, with a mean of 28.2 ounces and a standard deviation of 0.4 ounces. What percentage of filled boxes of rice have a weight less than 27.9 ounces?Find the z-table here.

A wildlife preserve features a crocodile with a documented age of 24 years, believed to be one of the oldest crocodiles in captivity. The lifespans of crocodiles have an approximately Normal distribution, with a mean of 18 years and a standard deviation of 2.6 years. What proportion of crocodiles have lifespans of at least 24 years?Find the z-table here.

The diameters of cherry tomatoes produced by a large farm have an approximately Normal distribution, with a mean diameter of 22 mm and a standard deviation of 2.5 mm. What proportion of such tomatoes have a diameter between 20 and 26 mm?Find the z-table here.

In a standard Normal distribution, what percentage of observations lie between z = –1.08 and z = 0.92?Find the z-table here.

The diameters of cherry tomatoes produced by a large farm have an approximately Normal distribution, with a mean diameter of 22 mm and a standard deviation of 2.5 mm. What proportion of such tomatoes have a diameter greater than 25 mm?Find the z-table here.