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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Name: ____________________ Date: ____________

1.Easy

Drag z so that the shaded area under the standard normal curve, to the left of z, is 0.0322. Find z to two decimals.

A = 0.0322

z =

2.Easy

The delivery times are normally distributed with mean 32 min and standard deviation 6 min. What fraction is above 29 min? Find P(X > x) as a decimal.

μ = 32σ = 6x = 29

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 16 of them is below 196.8 kg. Round z to two decimals.

μ = 12 kgσ = 0.8 kgn = 16< 196.8 kg

P =

4.Medium

The masses of passengers with luggage are independent and normal with mean 85 kg and standard deviation 12 kg. Find the probability P that the total mass of 10 of them is below 869 kg. Round z to two decimals.

μ = 85 kgσ = 12 kgn = 10< 869 kg

P =

5.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

6.Hard

The bag weights are normally distributed with mean 250 g and standard deviation 5 g. Find the value x below which 25% of them lie (the 25th percentile).

μ = 250σ = 5P = 25%

x = g

Answer key

1. z = −1.85
2. P(X > x) = 0.6915
3. P = 0.9332
4. P = 0.6915
5. x = 84.4 points
6. x = 246.6 g

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