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 0.9693. Find z to two decimals.

A = 0.9693

z =

2.Easy

The delivery times are normally distributed with mean 32 min and standard deviation 6 min. What fraction is above 25.1 min? Find P(X > x) as a decimal.

μ = 32σ = 6x = 25.1

P(X > x) =

3.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 9 of them is below 783 kg. Round z to two decimals.

μ = 85 kgσ = 12 kgn = 9< 783 kg

P =

4.Medium

The bag weights are normally distributed with mean 250 g and standard deviation 5 g. What fraction lies between 248.75 and 251 g? Give P as a decimal.

μ = 250σ = 5x₁ = 248.75x₂ = 251

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 exam scores are normally distributed with mean 65 points and standard deviation 10 points. Find the value x below which 90% of them lie (the 90th percentile).

μ = 65σ = 10P = 90%

x = points

Answer key

1. z = 1.87
2. P(X > x) = 0.8749
3. P = 0.6915
4. P = 0.178
5. P = 0.8413
6. x = 77.82 points

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