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.

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1.Easy

The heights of adult men are normally distributed with mean 178 cm and standard deviation 7 cm. What fraction is above 175.2 cm? Find P(X > x) as a decimal.

μ = 178σ = 7x = 175.2

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 bolts are independent and normal with mean 40 g and standard deviation 1.2 g. Find the probability P that the total mass of 9 of them exceeds 361.8 g. Round z to two decimals.

μ = 40 gσ = 1.2 gn = 9> 361.8 g

P =

4.Medium

The delivery times are normally distributed with mean 32 min and standard deviation 6 min. What fraction lies between 26 and 35 min? Give P as a decimal.

μ = 32σ = 6x₁ = 26x₂ = 35

P =

5.Hard

The IQ scores are normally distributed with mean 100 points and standard deviation 15 points. Find the value x below which 80% of them lie (the 80th percentile).

μ = 100σ = 15P = 80%

x = points

6.Hard

The heights of adult men are normally distributed with mean 178 cm and standard deviation 7 cm. Find the value x below which 5% of them lie (the 5th percentile).

μ = 178σ = 7P = 5%

x = cm

Answer key

1. P(X > x) = 0.6554
2. σ = 2.5 min
3. P = 0.3085
4. P = 0.5328
5. x = 112.6 points
6. x = 166.5 cm

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