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 IQ scores are normally distributed with mean 100 points and standard deviation 15 points. What fraction is above 118.75 points? Find P(X > x) as a decimal.

μ = 100σ = 15x = 118.75

P(X > x) =

2.Easy

The heights of adult men are normally distributed with mean 178 cm and standard deviation 7 cm. What fraction is below 183.95 cm? Find P(X < x) as a decimal.

μ = 178σ = 7x = 183.95

P(X < x) =

3.Medium

The masses of boxes are independent and normal with mean 12 kg and standard deviation 0.8 kg. Find the probability P that the total mass of 10 of them is below 117.5 kg. Round z to two decimals.

μ = 12 kgσ = 0.8 kgn = 10< 117.5 kg

P =

4.Medium

The battery lifetimes are normally distributed with mean 500 h and standard deviation 40 h. What fraction lies between 468 and 580 h? Give P as a decimal.

μ = 500σ = 40x₁ = 468x₂ = 580

P =

5.Hard

The mass X of a product from line 1 and Y from line 2 are independent and normal: X has mean 500 g and standard deviation 8 g, Y has mean 490 g and standard deviation 6 g. Find the probability P that X is greater than Y. Round z to two decimals.

μ_X = 500 g, σ_X = 8 gμ_Y = 490 g, σ_Y = 6 g

P =

6.Hard

The IQ scores are normally distributed with mean 100 points and standard deviation 15 points. Find the value x below which 25% of them lie (the 25th percentile).

μ = 100σ = 15P = 25%

x = points

Answer key

1. P(X > x) = 0.1056
2. P(X < x) = 0.8023
3. P = 0.1611
4. P = 0.7654
5. P = 0.8413
6. x = 89.88 points

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