A professor tells you that \( 20 \% \) of HCC students voted for Donald Trump in the last presidential election. You think that the percentage is lower than that. To test your claim, you first set these hypotheses: \( \mathrm{H}_{0}: p=0.2 ; \mathrm{H}_{\mathrm{a}}: p<0.2 \) You decide to use a significance level of \( \mathbf{1 0 \%} \). Then you randomly select 16 students and ask them who they voted for. The number who say they they voted for Donald Trump is 1 . Now calculate the sample proportion: \( \widehat{p}= \) (Round to 3 decimal places.) The P -value, which is the probability of getting a sample proportion as low as what you found assuming the null hypothesis is true, is 0.085 . What should you do with \( \mathrm{H}_{0} \) ? Reject null hypothesis Do not reject null hypothesis

Determine the area under the standard normal curve that lies to the left of (a) \( \mathrm{Z}=0.02 \), (b) \( \mathrm{Z}=-0.55 \), (c) \( \mathrm{Z}=0.83 \), and (d) \( \mathrm{Z}=0.87 \). (a) The area to the left of \( \mathrm{Z}=0.02 \) is (Round to four decimal places as needed.) (b) The area to the left of \( \mathrm{Z}=-0.55 \) is \( \square \). (Round to four decimal places as needed.) (c) The area to the left of \( \mathrm{Z}=0.83 \) is \( \square \). (Round to four decimal places as needed.) (d) The area to the left of \( \mathrm{Z}=0.87 \) is \( \square \). (Round to four decimal places as needed.)

The mean incubation time for a type of fertilized egg kept at a certain temperature is 25 days. Suppose that the incubation times are approximately norm 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 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 \( \square \). (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.

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.)

The mean incubation time for a type of fertilized egg kept at a certain temperature is 25 days. Suppose that the incubation fimes are approximately normally dis 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 10 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 \( \square \). (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.

(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.