Suppose the lengths of the pregnancies of a certain animal are approximately normally distributed with mean μ = 154 days and standard deviation σ = 16 days. Complete parts (a) through (f) below. ---**(a)** If 100 independent random samples of size n = 19 pregnancies were obtained from this population, we would expect ____ sample(s) to have a sample mean of 148 days or more.**(b)** If 100 independent random samples of size n = 19 pregnancies were obtained from this population, we would expect ____ sample(s) to have a sample mean of exactly 148 days.---**(d)** What is the probability that a random sample of 41 pregnancies has a mean gestation period of 148 days or less?The probability that the mean of a random sample of 41 pregnancies is less than 148 days is approximately ____. (Round 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 independent random samples of size n = 41 pregnancies were obtained from this population, we would expect ____ sample(s) to have a sample mean of exactly 148 days.- **B.** If 100 independent random samples of size n = 41 pregnancies were obtained from this population, we would expect ____ sample(s) to have a sample mean of 148 days or less.- **C.** If 100 independent random samples of size n = 41 pregnancies were obtained from this population, we would expect ____ sample(s) to have a sample mean of 148 days or more.---**(e)** What might you conclude if a random sample of 41 pregnancies resulted in a mean gestation period of 148 days or less?This result would be ______ so the sample likely came from a population whose mean gestation period is ____ 154 days.**(f)** What is the probability a random sample of size 15 will have a mean gestation period within 9 days of the mean?The probability that a random sample of size 15 will have a mean gestation period within 9 days of the mean is ____. (Round to four decimal places as needed.)

Given Information: Mean μ=154 days Standard deviation σ=16 days. To find the probability that a…

(d) What is the probability that a random sample of 41 pregnancies has a mean gestation period of 148 days or less? The probability that the mean of a random sample of 41 pregnancies is less than 148 days is approximately (Round to four decimal places as needed.)

(d) What is the probability that a random sample of 41 pregnancies has a mean gestation period of 148 days or less? The probability that the mean of a random sample of 41 pregnancies is less than 148 days is approximately (Round to four decimal places as needed.)

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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Concept explainers

Continuous Probability Distributions

Probability distributions are of two types, which are continuous probability distributions and discrete probability distributions. A continuous probability distribution contains an infinite number of values. For example, if time is infinite: you could count from 0 to a trillion seconds, billion seconds, so on indefinitely. A discrete probability distribution consists of only a countable set of possible values.

Normal Distribution

Suppose we had to design a bathroom weighing scale, how would we decide what should be the range of the weighing machine? Would we take the highest recorded human weight in history and use that as the upper limit for our weighing scale? This may not be a great idea as the sensitivity of the scale would get reduced if the range is too large. At the same time, if we keep the upper limit too low, it may not be usable for a large percentage of the population!

Question

Suppose the lengths of the pregnancies of a certain animal are approximately normally distributed with mean μ = 154 days and standard deviation σ = 16 days. Complete parts (a) through (f) below.

---

**(a)** If 100 independent random samples of size n = 19 pregnancies were obtained from this population, we would expect ____ sample(s) to have a sample mean of 148 days or more.

**(b)** If 100 independent random samples of size n = 19 pregnancies were obtained from this population, we would expect ____ sample(s) to have a sample mean of exactly 148 days.

---

**(d)** What is the probability that a random sample of 41 pregnancies has a mean gestation period of 148 days or less?

The probability that the mean of a random sample of 41 pregnancies is less than 148 days is approximately ____. (Round 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 independent random samples of size n = 41 pregnancies were obtained from this population, we would expect ____ sample(s) to have a sample mean of exactly 148 days.

- **B.** If 100 independent random samples of size n = 41 pregnancies were obtained from this population, we would expect ____ sample(s) to have a sample mean of 148 days or less.

- **C.** If 100 independent random samples of size n = 41 pregnancies were obtained from this population, we would expect ____ sample(s) to have a sample mean of 148 days or more.

---

**(e)** What might you conclude if a random sample of 41 pregnancies resulted in a mean gestation period of 148 days or less?

This result would be ______ so the sample likely came from a population whose mean gestation period is ____ 154 days.

**(f)** What is the probability a random sample of size 15 will have a mean gestation period within 9 days of the mean?

The probability that a random sample of size 15 will have a mean gestation period within 9 days of the mean is ____. (Round to four decimal places as needed.)

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