Normal distribution worksheet with answers

Free printable Normal distribution worksheet: 6 problems from easy to exam level, with an answer key. Print it or save it as a PDF.

New worksheet Practise online with hints

For teachers: free to print, copy and use in class. Every new worksheet has new values and its own answer key. A link to ExamProblems on your course page is appreciated.

Name: ____________________ Date: ____________

1.Easy

The heights of adult men are normally distributed with mean 178 cm and standard deviation 7 cm. What fraction is above 192.35 cm? Find P(X > x) as a decimal.

μ = 178σ = 7x = 192.35

P(X > x) =

2.Easy

Drag z so that the shaded area under the standard normal curve, to the left of z, is 0.3745. Find z to two decimals.

A = 0.3745

z =

3.Medium

The masses of bolts are independent and normal with mean 40 g and standard deviation 1.2 g. Find the probability P that the total mass of 12 of them exceeds 484.2 g. Round z to two decimals.

μ = 40 gσ = 1.2 gn = 12> 484.2 g

P =

4.Medium

The IQ scores are normally distributed with mean 100 points and standard deviation 15 points. What fraction lies between 70 and 130 points? Give P as a decimal.

μ = 100σ = 15x₁ = 70x₂ = 130

P =

5.Hard

The exam scores are normally distributed with mean 65 points and standard deviation 10 points. Drag the cut-off so the shaded bottom 80% is to the left of it. Find the cut-off x.

μ = 65 pointsσ = 10 points80%

x = points

6.Hard

The IQ scores are normally distributed with mean 100 points and standard deviation 15 points. Drag the cut-off so the shaded top 85% is to the right of it. Find the cut-off x.

μ = 100 pointsσ = 15 points85%

x = points

Answer key

1. P(X > x) = 0.02018
2. z = −0.32
3. P = 0.1562
4. P = 0.9545
5. x = 73.4 points
6. x = 84.4 points

Full step-by-step solutions: practise this topic on examproblems.com.