From the initial information we know that the estimated...

From the initial information we know that the estimated difference in the proportion of men minus women catching a cold is 0.13 (0.13 = 0.51- 0.38). Note that JMP may give the estimated difference in proportions as women - men (i.e. -0.13 = 0.38-0.51). What are the lower and upper bounds of the corresponding 95% CI for the probability of a man minus woman catching a cold (rounding to the nearest hundredth)?

Labs

Want to see this concept in action?

NEW

Explore this concept interactively to see how it behaves as you change inputs.

View Labs

Transcript

00:01 We are told in this question that time between colds, let's call that random variable x, is normally distributed with a mean of 160 days and a standard deviation of 40 days.

00:13 For question 1, we are asked for the probability of going 200 or more days between colds.

00:19 So this is the probability that x is at least 200.

00:25 Now suppose that this is our distribution for time between colds.

00:30 So it's normal and it has a mean of 1 ,000.

00:34 For question 1, we want the probability of going more than 200 days.

00:40 So that is equal to the area under the curve and to the right of 200.

00:48 Now since the total area underneath the curve is equal to 1, we can also write this as 1 minus the probability that x is less than 200.

01:01 So this term is the area to the left of 200.

01:11 And if we standardize this, this is equal to the probability that z is less than 200 minus 160 over 40.

01:31 That's 1 minus the probability that z is less than 1.

01:36 And if we look the probability that z is less than 1 up in the standard normal table, one corresponds to this cell.

01:47 It's 0 .8413.

01:53 And so we get 0 .1587.

01:59 So the probability of going 200 or more days between colds is .1587.

02:08 And the second question asks, what is the probability of going at least a year? so the probability that x is at least 365...

Question

Please give Ace some feedback