Question 1. Normally Distributed Data (using Excel or RStudio) In RStudio, we use the command pnorm(x,mu,sigma). The equivalent command in Excel is...

Question 1. Normally Distributed Data (using Excel or RStudio) 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 .) 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 . 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.