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 108.25 points? Find P(X > x) as a decimal.

μ = 100σ = 15x = 108.25

P(X > x) =

2.Easy

X and Y are independent normal variables for the time for two consecutive process steps: X has mean 12 min and standard deviation 1.5 min, Y has mean 20 min and standard deviation 2 min. Find the standard deviation σ of X + Y.

μ_X = 12 min, σ_X = 1.5 minμ_Y = 20 min, σ_Y = 2 min

σ = min

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 8 of them is below 94.9 kg. Round z to two decimals.

μ = 12 kgσ = 0.8 kgn = 8< 94.9 kg

P =

4.Medium

The battery lifetimes are normally distributed with mean 500 h and standard deviation 40 h. What fraction lies between 462 and 548 h? Give P as a decimal.

μ = 500σ = 40x₁ = 462x₂ = 548

P =

5.Hard

The IQ scores are normally distributed with mean 100 points and standard deviation 15 points. Find the value x below which 20% of them lie (the 20th percentile).

μ = 100σ = 15P = 20%

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 25% is to the right of it. Find the cut-off x.

μ = 100 pointsσ = 15 points25%

x = points

Answer key

1. P(X > x) = 0.2912
2. σ = 2.5 min
3. P = 0.3121
4. P = 0.7139
5. x = 87.38 points
6. x = 110.1 points

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