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Lesson Worksheet: Normal Distribution Mathematics

In this worksheet, we will practice using the normal distribution to calculate probabilities and find unknown variables and parameters.

Q1:

For the normal distribution shown, approximately what percent of data points lie in the shaded region?

Q2:

For a normally distributed data set with mean 32.1 and standard deviation 2.8, between which two values would you expect 95%‎ of the data set to lie?

  • A29.3 and 34.9
  • B17.5 and 28.7
  • C14.7 and 31.5
  • D26.5 and 37.7
  • E23.7 and 40.5

Q3:

Let 𝑍 be a standard normal random variable. Calculate 𝑃(0.54𝑍2.33).

Q4:

Let 𝑋 be a random variable which is normally distributed with mean 68 and standard deviation 3. Determine 𝑃(𝑋61.7).

Q5:

Given that 𝑍 is a standard normal random variable and 𝑃(𝑘𝑍1.98)=0.4283, find 𝑘.

Q6:

Suppose 𝑍 is a standard normal random variable. Given 𝑃(𝑍𝑘)=0.9922, find the value of 𝑘.

Q7:

Let 𝑋 be a random variable which is normally distributed with mean 63 and variance 144. Determine 𝑃(37.56𝑋57.36).

Q8:

Suppose 𝑋 is normally distributed with mean 𝜇 and variance 196. Given that 𝑃(𝑋40)=0.0668, find the value of 𝜇.

Q9:

Let 𝑋 be a random variable which is normally distributed with mean 𝜇=75 and standard deviation 𝜎=6. Given that 𝑃(𝑋𝑘)=0.9938, find 𝑘.

Q10:

Let 𝑋 be a normal random variable. Find 𝑃(𝜇0.56𝜎<𝑋<𝜇+1.64𝜎).

This lesson includes 47 additional questions and 341 additional question variations for subscribers.

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