I need help figuring out these two problems. I think I have the right idea about solving them but I'm not exactly sure.

8. Two companies market new batteries targeted at owners of personal music players. DuraTunes claimes a mean battery life of 11 hours, while RockReady advertises 12 hours.

-Suppose the standard deviations are 2hours for DuraTunes and 1.5 hours for RockReady. You are headed for 8 hours at the beach. Which battery is most likely to last all day? Explain.

10. John Beale of Stanford< CA, recorded the speeds of cars driving past his house, where the speed limit read 20 mph. The mean of 100 readings was 23.84 mph, with a standard deviation of 3.56 mph. (He actually recorded every car for a 2-month period. These are 100 representative readings.)

- How many standard deviations from the mean would a car going under the speed limit be?

For problem 8, to determine which battery is most likely to last all day, we need to compare the hours of battery life claimed by DuraTunes and RockReady with your desired battery life of 8 hours at the beach.

First, let's find the z-scores for each battery. The z-score tells us how many standard deviations a particular value is from the mean.

For DuraTunes:
z-score = (desired battery life - mean battery life) / standard deviation
z-score = (8 - 11) / 2
z-score = -3 / 2
z-score = -1.5

For RockReady:
z-score = (desired battery life - mean battery life) / standard deviation
z-score = (8 - 12) / 1.5
z-score = -4 / 1.5
z-score = -2.67

The z-score represents the number of standard deviations below the mean. In this case, we're looking for the battery that is most likely to last all day, which means we are interested in the battery with a z-score closest to zero.

Comparing the z-scores, we see that DuraTunes has a z-score of -1.5 while RockReady has a z-score of -2.67. Since -1.5 is closer to zero than -2.67, it means that DuraTunes is more likely to last all day at the beach.

For problem 10, to determine how many standard deviations a car going under the speed limit would be, we need to calculate the z-score again.

z-score = (observed speed - mean speed) / standard deviation
z-score = (20 - 23.84) / 3.56
z-score = -3.84 / 3.56
z-score = -1.08

Since the z-score represents the number of standard deviations, a car going under the speed limit would be approximately 1.08 standard deviations below the mean speed.