In a large population of birds, the proportion of Cockatoos is5APLet be the random variable that represents the sample proportion of Cockatoos forsamples of size n drawn from the population.AFind the smallest integer value of n such that the standard deviation of p is less thanor equal to 1%.

Suppose p is the true proportion of Cockatoos.

Answered: In a large population of birds, the…

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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The weight of a loaf of bakery bread at the grocery store follows a Normal distribution with a mean of μ = 12 ounces and a standard deviation of σ = 1 ounce. Suppose we pick four loaves at random from the bin and find their total weight, W. Which of the following statements describes the random variable W? O The random variable W is binomial, with a mean of 48 ounces and a standard deviation of two ounces. O The random variable W is binomial, with a mean of 12 ounces and a standard deviation of two ounces. O The random variable W is Normal, with a mean of 12 ounces and a standard deviation of one ounce. O The random variable W is Normal, with a mean of 48 ounces and a standard deviation of two ounces. O The random variable W is Normal, with a mean of 48 ounces and a standard deviation of four ounces.
If x represents a random variable with mean 131 and standard deviation 40, then the standard deviation of the sampling distribution of the means with sample size 100 is 4. O True O False
A simple random sample is taken from a population and yields the following data for a variable of the population. 37 36 16 16 19 31 Find a point estimate for the population standard deviation (that is, the standard deviation of the variable). 12 26 39 9 A point estimate for the population standard deviation is (Round to two decimal places as needed.)
A random sample of size 18is to be taken from a population that is normally distributed with mean 45 and standard deviation 10. The sample mean of the observations in our sample is to be computed. The sampling distribution of the sample mean is.....
The mean weight of a fire ant worker is 3.11 mg with a standard deviation of .49 mg. Suppose we randomly select 14 different fire ant workers having weights F1, F2, , F14. Let S = F1 + F2 + ...+F14 and let M = S/14. This means S is the sample sum and M is the sample mean of the selected ant weights. (Note: random selection means F1 F14 are independent.). Assume the Fis are normally distributed. j) What is the expected value of M - 3.11 ? k) What is the standard deviation of [(M - 3.11)/49]/srt14
The fracture strength of bi-tempered glass averages 14.03 (measured in thousands of pounds per square inch) and has standard deviation 2. Suppose we randomly select 100 pieces of bi-tempered glass. Let M be the random variable representing the mean fracture strength of the 100 selected pieces. Let T be the random variable representing the sum of the fracture strengths of the 100 selected pieces. Using R and write the code outa) What theorem will let us treat T and M as approximately normal random variables? Monte Carlo TheoremLaw of Large Numbers 301 TheoremCentral Limit TheoremChebychev's TheoremConvolution Theorem b) What is the expected value of T? c) What is the standard deviation of T? d) What is the approximate probability that T is greater than 1400? e) What is the 98th percentile of the approximate distribution of T? f) What is the standard deviation of M? g) What is the approximate probability M is greater than 13.99? h) What is the variance of 93M?
Let x be a random variable representing the starting salary of a first-year teacher in a city. A report claims that the mean starting salary of these first-year teachers is greater than $50,000. To test this claim we find that a random sample of 20 teachers has a mean starting salary of $51,425 with a sample standard deviation of $3,549. If you assume that the population mean is $50,000, find the P-value corresponding to the hypothesis that the mean starting salary of the first-year teachers is greater than $50,000.
Let x be a random variable representing the starting salary of a first-year teacher in a city. A report claims that the mean starting salary of these first-year teachers is less than $52,000. To test this claim we find that a random sample of 25 teachers has a mean starting salary of $51,875 with a sample standard deviation of $1,055. If you assume that the population mean is $52,000, find the P-value corresponding to the hypothesis that the mean starting salary of the first-year teachers is less than $52,000. A. 0.28 B. 0.56 C. 0.14 D. 0.36
Three randomly selected households are surveyed. The numbers of people in the households are 1,2 and 12. assume that sample of size n=2 are randomly selected with replacement from the population of 1,2, and 12. nine different samples: 1,1, 1,2 1,12, 2,1 2,2 2,12 12,1 12,2 12,12 Find the variance of each of the nine samples, then summarize the sampling distribution of the variances in the format of a table representing the probability distribution of the distinct variance values.
In a study of life expectancy in a certain region, the mean age at death was 70 years, and the standard deviation was 5 years. The life expectancy (years) is assumed to follow a skewed distribution. Suppose that a random sample of 45 people from this region is selected. The mean life expectancy (years) of the sample is considered a random variable. What is its standard error? 0.5976 O 2.2361 O 5.2341 O 0.1111
The weight of a male bald eagle has approximately a normal distribution with mean ?= 7.4 pounds and a standard deviation of ?= 1.6 pounds. Suppose we take a random sample of n=64 male bald eagles. Let X̄ be the random variable representing the mean weight in pounds of the 64 sampled male bald eagles. Let Xtot be the random variable representing sum of the weights of the 84 sampled bald eagles. a) About what proportion of male bald eagles have weights between 7.0 and 7.8 pounds? b) About what proportion of male bald eagles have weights greater than 7.8 pounds? c) About how many of the 64 sampled male bald eagles would you expect to have weight greater than 7.8 pounds? (nearest integer)? d) About how many of the 64 sampled male bald eagles would you expect to have weight between 7.0 and 7.8 pounds? (nearest integer)? e) What is the standard deviation of the distribution of X̄ (in pounds)? f) What is the standard deviation of the distribution of Xtot (in pounds)? g) What is the…

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