It is known that the weights of male Persian cats are normally distributed with mean 6.1 kgand variance 0.5²kg².(a) Sketch a diagram showing the above information.(b)Find the proportion of male Persian cats weighing between 5.5kg and 6.5kg.A group of 80 male Persian cats are drawn from this population.(c)Determine the expected number of cats in this group that have a weight of lessthan 5.3 kg.(d)It is found that 12 of the cats weigh more than xkg. Estimate the value of x.(e) Ten of the cats are chosen at random. Find the probability that exactly one of themweighs over 6.25 kg.

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Answered: It is known that the weights of male…

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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An ecologist is studying the impact of local polluted waters on the growth of alligators. The length of adult male alligators typically follows a normal distribution with a standard deviation of 2 feet. The ecologist wants to estimate the mean length of this population of alligators. Suppose she samples n alligators at random and uses the sample mean, X to as an estimator for u. a. What is the bias and variance of the estimator? (Note, these may be a function of n.) b. If n = 4, what is the probability that the estimator is within one foot of the true mean? (I.e. find P(|X – µ| < 1). c. What sample size, n, is required for the estimator to be within one foot of the true mean with 95% probability? (I.e. find the value of n that satisfies P(|X – µ| < 1) = 0.95.) d. Suppose the ecologist ends up sampling n = 9 alligators and calculates a sample mean of ī = 10.4 feet. Construct a 95% confidence interval for the population mean. e. Give an interpretation for the interval obtained in (d).
4. It is known that the average weight of babies born in a maternity ward is 3.2 kg and the variance of 0.09 kg 2corresponds to the normal distribution. According to this; a) Assuming that an average of 200 babies are born a day, how many of these babies weigh more than 4 kg? b) What weight is the lightest 5% lighter than babies?
A manufacturer of bolts has a quality control policy that requires it to destroy any bolts that are more than 2 standard deviations from the mean. A sample of 15 bolts were tested and their variance was recorded to be 10. Stating any assumptions you need to make, test, at the 5% level, whether the bolts are meeting the established standard.
Suppose a batch of steel rods produced at a steel plant have a mean length of 187 milimeters, and a Variance of 64. If 416 rods are sampled at random from the batch, what is the probability that the mean length all the sample rods would differ from the population mean by less than 0.65 millimeters? Round your answer to four decimal places.
Suppose the number of off springs a female eagle raises during its lifetime has a distribution with mean 15 and variance 4. In an area, 45 rescued and cured female eagles are set free. If these eagles are assumed to be independent (no lack of male partners and food resources), the total number of off-springs produced by these eagles can be assumed to have a Normal distribution with mean and variance
The amount of chlorine in 100 cm3 water taken from a water tank was measured, the average was 2.15 mg was found. The expert claims that the amount of chlorine in the water is greater than that measured. For this reason, 100 households were randomly selected, with an average chlorine content of 2.55mg and a variance of 0.49 mg. According to this data, find the account value z. 13 - O A) 8,15 O B) 5,71 O C) -5,71 O D) -8, 15 O E) 0.54
The results of a state mathematics test for random samples of students taught by two different teachers at the same school are shown below. Can you conclude there is a difference in the mean mathematics test scores for the students of the two teachers? Use α = 0.01. In addition, assume the populations are normally distributed and the population variances/standard deviations are not equal. Teacher 1 Teacher 2 ?̅1 = 473 ?̅2 = 459 S1 = 39.7 S2 = 24.5 n 1 = 8 n 2 = 18 a. State the null and alternate hypotheses (write it mathematically) and write your claim. b. Find the test statistic c. Identify the Rejection region (critical region) and fail to reject region. Show this by drawing a curve and…
The heights of men in a certain city are normally distributed with a mean of 275 cm and a variance of 25cm. Compute the minimum height for the top sixteen percent of the men in the city.
We want to estimate the mean distance travelled to work by employees of a large manufacturing firm. Past studies indicate that the variance of these distances is 4.0 km2and that the distances follow a normal distribution. How many employees should be chosen at random and polled if the estimated mean distance is to be within 0.1 km ofthe true mean with a confidence level of 95%?
Actuaries use various parameters when evaluating the cost of a life insurance policy. The variance of the life spans of a population is one of the parameters used for the evaluation. Each year, the actuaries at a particular insurance company randomly sample 30 people who died during the year (with the samples chosen independently from year to year) to see whether the variance of life spans has changed. The life span data from this year and from last year are summarized below. Current Last Year Year *1 = 75.8 x2 = 76.2 s3 = 47.61 s3= 92.16 (The first row gives the sample means and the second row gives the sample variances.) Assume that life spans are approximately normally distributed for each of the populations of people who died this year and people who died last year. Can we conclude, at the 0.05 significance level, that the variance of the life span for the current year, of, differs from the variance of the life span for last year, o,? Perform a two-tailed test. Then complete the…
The F-statistic is a ratio score resulting in a measure of the estimated proportion of variance due to the independent variable. True or false
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