# Two probability and hypothesis testing questions

Question 5: The weight of bags "checked in" is normal, with a mean of 30 pounds and a standard deviation of 9 pounds.

a) What is the probability that a randomly selected bag will weigh more than 48 pounds?

b) What is the probability that the total weight of 4 bags will be more than 192 pounds?

c) Find the probability that a sample of 81 bags will average more than 32 pounds.

d) If a sample of 36 bags showed the mean to be 33 pounds, can you conclude that the average weight has changed? (use alpha = 0.05)

Question 6: Test the hypothesis that more than 60 percent of the U.S. senators (of a total 100 senators) favor the president's economic plan, if a sample of 40 showed that 22 favor the plan (use alpha = .05).

#### Solution Preview

Question 5

The weight of bags "checked in" is normal, with a mean of 30 pounds and a standard deviation of 9 pounds.

a) What is the probability that a randomly selected bag will weigh more than 48 pounds?

For this problem, we're going to use z-scores. To calculate a z-score, use the following formula:

.

where x is the score to be converted into a z-score, σ is the standard deviation of the population, and μ is the mean of the population

For this problem, μ = 30, σ = 9, and x = 48. Calculate the z-score:

z = (48 - 30)/9 = 18/9 = 2

Now, look at a z-distribution table to see the probability associated with this z-score. This is equivalent to finding the area under the z-distribution curve to the right of z = 2. You should find that the p-value/area under the curve is equal to p = 0.0228.

This means that the probability that a randomly selected bag will weigh more than 48 pounds is 0.0228 or 2.28%.

b) What is the probability that the total weight of 4 bags will be more than 192 pounds?

Now that we have a sample size, we can use a different formula for ...