An automobile manufacturer has given its van a 31.0 miles/gallon (MPG) rating. An independent testing firm has been contracted to test the actual MPG for this van since it is believed that the van performs under the manufacturer's MPG rating. After testing 150 vans, they found a mean MPG of 30.8. Assume the population standard deviation is known to be 2.1 . Is there sufficient evidence at the 0.02 level to support the testing firm's claim? Step 5 of 6 : Identify the level of significance for the hypothesis test.

The mean IQ of statistics teachers is greater than 120. Identify the type I and type II errors for the hypothesis test of this claim.

Find the z-scores that separate the middle \( 19 \% \) of the distribution from the area in the tails of the standard normal distribution. The z-scores are (Use a comma to separate answers as needed. Round to two decimal places as needed.)

Assume the random variable X is normally distributed, with mean \( \mu=53 \) and standard deviation \( \sigma=8 \). Find the 9th percentile. The 9th percentile is (Round to two decimal places as needed.)

(Round to the nearest integer as needed.) A. If 100 fertilized eggs were randomly selected, 34 of them would be expected to hatch in less than 23 days. B. If 100 fertilized eggs were randomly selected, exactly \( \square \) would be expected to hatch on day 23. C. In every group of 100 fertilized eggs, \( \square \) eggs would be expected to hatch in less than 23 days. (c) Find and interpret the probability that a randomly selected fertilized egg takes over 27 days to hatch. The probability that a randomly selected fertilized egg takes over 27 days to hatch is (Round to four decimal places as needed.) Interpret this probability. Select the correct choice below and fill in the answer box to complete your choice. (Round to the nearest integer as needed.) A. If 100 fertilized eggs were randomly selected, exactly \( \square \) would be expected to hatch on day 27 . B. If 100 fertilized eggs were randomly selected, \( \square \) of them would be expected to take more than 27 days to hatch. C. In every group of 100 fertilized eggs, \( \square \) eggs would be expected to hatch in more than 27 days.

(c) Suppose the area under the normal curve to the right of \( \mathrm{X}=4670 \) is 0.0228 . Provide an interpretation of this result. Select the correct 0 (Type a whole number.) A. The probability is 0.0228 that the birth weight of a randomly chosen full-term baby in this population is less than grams. B. The probability is 0.0228 that the birth weight of a randomly chosen full-term baby in this population is more than grams.