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.
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