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

Drag z so that the shaded area under the standard normal curve, to the left of z, is 0.8186. Find z to two decimals.

A = 0.8186

z =

2.Easy

Drag z so that the shaded area under the standard normal curve, to the left of z, is 0.8106. Find z to two decimals.

A = 0.8106

z =

3.Medium

X is normal with mean 120 mm and standard deviation 0.3 mm; Y is independent and normal with mean 80 mm and standard deviation 0.4 mm. Find the probability P that X + Y is more than 199.8 mm. Round z to two decimals.

μ_X = 120, σ_X = 0.3μ_Y = 80, σ_Y = 0.4X + Y > 199.8 mm

P =

4.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 4 of them is below 98.5 kg. Round z to two decimals.

μ = 25 kgσ = 0.5 kgn = 4< 98.5 kg

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 heights of adult men are normally distributed with mean 178 cm and standard deviation 7 cm. Find the value x below which 99% of them lie (the 99th percentile).

μ = 178σ = 7P = 99%

x = cm

Answer key

1. z = 0.91
2. z = 0.88
3. P = 0.6554
4. P = 0.06681
5. P = 0.8413
6. x = 194.3 cm

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