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Suppose the lengths of the pregnancies of a certain animal are approximately normally distributed with mean u= 296 days and standard deviation o = 30 days. Complete parts (a) through (f) below Click here to view the standard normal distribution table (page 1). Click here to view the standard normal distribution table (page 2). TITE provavmy urat a TanuUmy serecieu pregnancy lasiS ess ula 204 uays Is apprUAatery J440 Ruuru Lnanaau SP sanpid iPnan innL Interpret this probability. Select the correct choice below and fill in the answer box within your choice. (Round to the nearest integer as needed) O A. If 100 pregnant individuals were selected independently from this population, we would expect pregnancies to last exactly 284 days. O B. If 100 pregnant individuals were selected independently from this population, we would expect pregnancies to last more than 284 days. CC. If 100 pregnant individuals were selected independently from this population, we would expect 34 pregnancies to last less than 284 days (b) Suppose a random sample of 18 pregnancies is obtained. Describe the sampling distribution of the sample mean length of pregnancies. The sampling distribution of x is with u; = 296 and a: = 7.0711. normal (Round to four decimal places as needed.) (c) What is the probability that a random sample of 18 pregnancies has a mean gestation period of 284 days or less? The probability that the mean of a random sample of 18 pregnancies is less than 284 days is approximately (Round to four decimal places as needed)

Suppose the lengths of the pregnancies of a certain animal are approximately normally distributed with mean u= 296 days and standard deviation o = 30 days. Complete parts (a) through (f) below Click here to view the standard normal distribution table (page 1). Click here to view the standard normal distribution table (page 2). TITE provavmy urat a TanuUmy serecieu pregnancy lasiS ess ula 204 uays Is apprUAatery J440 Ruuru Lnanaau SP sanpid iPnan innL Interpret this probability. Select the correct choice below and fill in the answer box within your choice. (Round to the nearest integer as needed) O A. If 100 pregnant individuals were selected independently from this population, we would expect pregnancies to last exactly 284 days. O B. If 100 pregnant individuals were selected independently from this population, we would expect pregnancies to last more than 284 days. CC. If 100 pregnant individuals were selected independently from this population, we would expect 34 pregnancies to last less than 284 days (b) Suppose a random sample of 18 pregnancies is obtained. Describe the sampling distribution of the sample mean length of pregnancies. The sampling distribution of x is with u; = 296 and a: = 7.0711. normal (Round to four decimal places as needed.) (c) What is the probability that a random sample of 18 pregnancies has a mean gestation period of 284 days or less? The probability that the mean of a random sample of 18 pregnancies is less than 284 days is approximately (Round to four decimal places as needed)

Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018
Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018
18th Edition
ISBN:9780079039897
Author:Carter
Publisher:Carter
Chapter10: Statistics
Section10.3: Measures Of Spread
Problem 26PFA
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11 Part C

**Normal Distribution and Probability in Animal Gestation** Suppose the lengths of the pregnancies of a certain animal are approximately normally distributed with a mean (μ) of 296 days and a standard deviation (σ) of 30 days. Complete the following parts: **Click to view the standard normal distribution table (page 1).** **Click to view the standard normal distribution table (page 2).** ### Part (a) The probability that a randomly selected pregnancy lasts less than 284 days is approximately **0.3446** (rounded to four decimal places as needed). **Interpret this probability:** Select the correct choice below and fill in the answer box within your choice. (Round to the nearest integer as needed.) - **A.** If 100 pregnant individuals were selected independently from this population, we would expect __ pregnancies to last exactly 284 days. - **B.** If 100 pregnant individuals were selected independently from this population, we would expect __ pregnancies to last more than 284 days. - **C.** If 100 pregnant individuals were selected independently from this population, we would expect **34** pregnancies to last less than 284 days. ### Part (b) **Suppose a random sample of 18 pregnancies is obtained. Describe the sampling distribution of the sample mean length of pregnancies.** The sampling distribution of \( \bar{x} \) is normal with \( \mu_{\bar{x}} = 296 \) and \( \sigma_{\bar{x}} = 7.0711 \). (Round to four decimal places as needed.) ### Part (c) What is the probability that a random sample of 18 pregnancies has a mean gestation period of 284 days or less? The probability that the mean of a random sample of 18 pregnancies is less than 284 days is approximately __ (round to four decimal places as needed). **Instructions:** Enter your answer in the answer box and then click "Check Answer".
Transcribed Image Text:**Normal Distribution and Probability in Animal Gestation** Suppose the lengths of the pregnancies of a certain animal are approximately normally distributed with a mean (μ) of 296 days and a standard deviation (σ) of 30 days. Complete the following parts: **Click to view the standard normal distribution table (page 1).** **Click to view the standard normal distribution table (page 2).** ### Part (a) The probability that a randomly selected pregnancy lasts less than 284 days is approximately **0.3446** (rounded to four decimal places as needed). **Interpret this probability:** Select the correct choice below and fill in the answer box within your choice. (Round to the nearest integer as needed.) - **A.** If 100 pregnant individuals were selected independently from this population, we would expect __ pregnancies to last exactly 284 days. - **B.** If 100 pregnant individuals were selected independently from this population, we would expect __ pregnancies to last more than 284 days. - **C.** If 100 pregnant individuals were selected independently from this population, we would expect **34** pregnancies to last less than 284 days. ### Part (b) **Suppose a random sample of 18 pregnancies is obtained. Describe the sampling distribution of the sample mean length of pregnancies.** The sampling distribution of \( \bar{x} \) is normal with \( \mu_{\bar{x}} = 296 \) and \( \sigma_{\bar{x}} = 7.0711 \). (Round to four decimal places as needed.) ### Part (c) What is the probability that a random sample of 18 pregnancies has a mean gestation period of 284 days or less? The probability that the mean of a random sample of 18 pregnancies is less than 284 days is approximately __ (round to four decimal places as needed). **Instructions:** Enter your answer in the answer box and then click "Check Answer".
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