Lesson Worksheet: Normal Distribution Mathematics
In this worksheet, we will practice using the normal distribution to calculate probabilities and find unknown variables and parameters.
Q6:
For a normally distributed data set, approximately what percent of data points will lie within two standard deviations of the mean?
Q7:
For a normally distributed data set with mean 32.1 and standard deviation 2.8, between which two values would you expect of the data set to lie?
- A26.5 and 37.7
- B23.7 and 40.5
- C20.3 and 25.9
- D14.7 and 31.5
- E29.3 and 34.9
Q16:
Let be a random variable which is normally distributed with mean and standard deviation . Given that , find .
Q17:
Let be a random variable which is normally distributed with mean and standard deviation . Given that and , calculate the values of and .
- A,
- B,
- C,
- D,
Q18:
Let be a random variable which is normally distributed with and . Given that , find .
Q19:
Let be a random variable which is normally distributed with mean 60 and standard deviation 5. Determine .
Q20:
Let be a normal random variable. Find .
Q21:
Let be a normal random variable. Find .
Q22:
Let be a random variable which is normally distributed with mean 73 and standard deviation 15. Determine .
Q23:
Let be a random variable which is normally distributed with mean and standard deviation . Given that and , find the value .
Q24:
Let be a random variable which is normally distributed with standard deviation 10. Given that , find the mean of .
Q25:
Let be a normal random variable such that and . Calculate .