Mean is 222Standard Dev is 19Question is asking me to use technology to find the answer to this problem. Can you explain how to do this such as with either the Graphing calculator and Excel? (c) What is the probability that a random sample of 19 pregnancies has a mean gestation period of 215 days or less?Notice that the probability in this case is for the mean of a sample of the population. This means that the sampling distribution of the mean should be used and not the population distribution.In part (b), the sample mean (\( \mu_{\bar{x}} \)) was calculated to be 222 and the standard deviation (\( \sigma_{\bar{x}} \)) was calculated to be 4.358899. Therefore, the sampling distribution of \( \bar{x} \) for a sample size of 19 is approximately normal with a mean \( \mu_{\bar{x}} = 222 \) and a standard deviation \( \sigma_{\bar{x}} = 4.358899 \). While either technology or a standard normal distribution table could be used to calculate the desired probability, in this problem, use technology.

Given that: Sample size, n=19 Mean, μx¯=222 Standard deviation, σx¯=4.358899(c) Compute the probability that a random sample of 19 pregnancies has a mean gestation period of 215 days or less: For this, first convert this into standard normal using z-score: z=x-μx¯σx¯=x-μσn Px¯≤215=Px-μσn≤215-2221919=PZ≤-74.358899=PZ≤-1.6059 Determine the probability by using the following excel function: "=NORM.S.DIST(z, cumulative)" Px≤215=PZ≤-6.99=0.05 Thus, the required probability is 0.05.

Answered: (c) What is the probability that a…

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

See similar textbooks

Related questions

Question

Mean is 222

Standard Dev is 19

Question is asking me to use technology to find the answer to this problem. Can you explain how to do this such as with either the Graphing calculator and Excel?

(c) What is the probability that a random sample of 19 pregnancies has a mean gestation period of 215 days or less?

Notice that the probability in this case is for the mean of a sample of the population. This means that the sampling distribution of the mean should be used and not the population distribution.

In part (b), the sample mean (\( \mu_{\bar{x}} \)) was calculated to be 222 and the standard deviation (\( \sigma_{\bar{x}} \)) was calculated to be 4.358899. Therefore, the sampling distribution of \( \bar{x} \) for a sample size of 19 is approximately normal with a mean \( \mu_{\bar{x}} = 222 \) and a standard deviation \( \sigma_{\bar{x}} = 4.358899 \). While either technology or a standard normal distribution table could be used to calculate the desired probability, in this problem, use technology.

Definition Definition Measure of central tendency that is the average of a given data set. The mean value is evaluated as the quotient of the sum of all observations by the sample size. The mean, in contrast to a median, is affected by extreme values. Very large or very small values can distract the mean from the center of the data. Arithmetic mean: The most common type of mean is the arithmetic mean. It is evaluated using the formula: μ = 1 N ∑ i = 1 N x i Other types of means are the geometric mean, logarithmic mean, and harmonic mean. Geometric mean: The nth root of the product of n observations from a data set is defined as the geometric mean of the set: G = x 1 x 2 ... x n n Logarithmic mean: The difference of the natural logarithms of the two numbers, divided by the difference between the numbers is the logarithmic mean of the two numbers. The logarithmic mean is used particularly in heat transfer and mass transfer. ln x 2 − ln x 1 x 2 − x 1 Harmonic mean: The inverse of the arithmetic mean of the inverses of all the numbers in a data set is the harmonic mean of the data. 1 1 x 1 + 1 x 2 + ...

Expert Solution