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 0.9418. Find z to two decimals.

A = 0.9418

z =

2.Easy

X and Y are independent normal variables for the length of part A plus part B in an assembly: X has mean 120 mm and standard deviation 0.3 mm, Y has mean 80 mm and standard deviation 0.4 mm. Find the standard deviation σ of X + Y.

μ_X = 120 mm, σ_X = 0.3 mmμ_Y = 80 mm, σ_Y = 0.4 mm

σ = mm

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 16 of them exceeds 649.6 g. Round z to two decimals.

μ = 40 gσ = 1.2 gn = 16> 649.6 g

P =

4.Medium

The battery lifetimes are normally distributed with mean 500 h and standard deviation 40 h. What fraction lies between 436 and 550 h? Give P as a decimal.

μ = 500σ = 40x₁ = 436x₂ = 550

P =

5.Hard

The bag weights are normally distributed with mean 250 g and standard deviation 5 g. Find the value x below which 97.5% of them lie (the 97.5th percentile).

μ = 250σ = 5P = 97.5%

x = g

6.Hard

The exam scores are normally distributed with mean 65 points and standard deviation 10 points. Find the value x below which 99% of them lie (the 99th percentile).

μ = 65σ = 10P = 99%

x = points

Answer key

1. z = 1.57
2. σ = 0.5 mm
3. P = 0.02275
4. P = 0.8396
5. x = 259.8 g
6. x = 88.26 points

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