Question 1. Normally Distributed Data (using Excel or RStudio - your choice!) No

Question

Question 1. Normally Distributed Data (using Excel or RStudio - your
choice!)
Note: In RStudio, we use the command pnorm(x,mu,sigma). The equivalent command
in Excel is =NORM.DIST(x,mu,sigma,1) (the “1” at the end is required).

1. I bike to work in the summer and my travel time can be shown (because I tracked
it...) to be normally distributed with a mean of 14 minutes and a standard
deviation of 2 minutes. If I leave the house at 8:13 and I have to be at work at
8:30, what is the probability that I will be late?

2. It is possible to model human brain capacity using a normal distribution. Assume
that the mean brain capacity is 0.9 Megapixels with a standard deviation of 0.05
Megapixels. What is the probability that a randomly chosen person would have a
brain capacity less than 1 Megapixel? Greater than 1 Megapixels?

3. Men’s heights are normally distributed with a mean of 70 inches and standard
deviation of 2.9 inches. My friend Justin is 6 feet, 3 inches tall - use the idea of
p-values to determine if he is particularly tall.

4. Women’s heights are normally distributed with a mean of 64 inches and standard
deviation of 2.7 inches. My colleague Lorna is 5 feet, 2 inches tall - use the idea of
p-values to determine if she is particularly short.

5. I have a group of four male friends that gets together to play board games (of
course I do). They are (1) 6 feet, 0 inches, (2) 5 feet, 10 inches tall, (3) 6 feet, 1
inch tall and (4) 5 feet, 11.5 inches tall (he would claim 6 feet exactly, but we
measured - it isn’t true). Use the idea of p-values to determine if my
group of 4 male friends is particularly tall.

Explanation / Answer

Difference in time =30-13=17

Hence we need P(x> 17)

When x is normally distributed with mean =14, sd=2

=1-norm.dist(17,14,2,1)

0.0668

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