BSB123 Data Analysis

Binomial and Normal Distributions

Show all formulas and calculations. If you do the calculations in Excel please copy across the relevant Table/Output

Question One

A university teaching room has a capacity to hold 50 students. The probability that any one student attends the teaching room during class is 0.7. If 50 students are enrolled in the class, calculate the probability that:

1. Exactly 40 attend the class
2. Fewer than 30 attend the class
3. Between 30 and 40 (inclusive) attend the class (Check: 0.912)
4. More than 10 students do not attend the class

Question Two

A manufacturing process produces tyres with a lifetime that is normally distributed with a mean of 60,000km and a standard deviation of 10,000km. Using excel, calculate the following (including a picture of the area under the curve for a. to c.)

1. The probability that any one tyre lasts longer than 75,000km.
2. The probability that any one tyre lasts between 45,000 and 65,000km.
3. The probability that any one tyre lasts less than 72,500km.
4. The lifespan of the bottom 15% of tyres?
5. If two tyres are selected at random so that they would be considered independent of each other, what is the probability that both last longer than 50,000km. (check: 0.708)