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 0.1660. Find z to two decimals.

A = 0.1660

z =

2.Easy

The IQ scores are normally distributed with mean 100 points and standard deviation 15 points. What fraction is below 107.5 points? Find P(X < x) as a decimal.

μ = 100σ = 15x = 107.5

P(X < x) =

3.Medium

The masses of bags of cement are independent and normal with mean 25 kg and standard deviation 0.5 kg. Find the probability P that the total mass of 10 of them is below 248.4 kg. Round z to two decimals.

μ = 25 kgσ = 0.5 kgn = 10< 248.4 kg

P =

4.Medium

The heights of adult men are normally distributed with mean 178 cm and standard deviation 7 cm. What fraction lies between 176.25 and 183.6 cm? Give P as a decimal.

μ = 178σ = 7x₁ = 176.25x₂ = 183.6

P =

5.Hard

The heights of adult men are normally distributed with mean 178 cm and standard deviation 7 cm. Find the value x below which 97.5% of them lie (the 97.5th percentile).

μ = 178σ = 7P = 97.5%

x = cm

6.Hard

The IQ scores are normally distributed with mean 100 points and standard deviation 15 points. Drag the cut-off so the shaded bottom 25% is to the left of it. Find the cut-off x.

μ = 100 pointsσ = 15 points25%

x = points

Answer key

1. z = −0.97
2. P(X < x) = 0.6915
3. P = 0.1562
4. P = 0.3869
5. x = 191.7 cm
6. x = 90 points

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