The mean and standard deviation of height of an elf in Chrismas land are u = 161 cm and o = 40 cm, respectively. From the set of elfsn = 210 individuals are chosen at random independently of each other, and from this sample we calculate the average height of an elf.Calculate the random average's:(a) expected value:(b) standard deviation:Use the normal approximation to estimate the probability that the random average(c) is at least 166 cm:(d) belongs to the interval 156-163 cm:Give an exact answer or round it to three decimal places. Use dot as a decimal separator.

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Answered: The mean and standard deviation of…

A First Course in Probability (10th Edition)

10th Edition

ISBN:9780134753119

Author:Sheldon Ross

Publisher:Sheldon Ross

Chapter1: Combinatorial Analysis

Section: Chapter Questions

Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...

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Assume that ﬁnal exam scores in a given course are approximately normally distributed with a mean of 75 and a standard deviation of 10 points. In a class of 200 students, how many would you expect to fail the exam (i.e., score less than 60) (note: scores can only be approximately normally distributed, because the minimum score is 0, but this should not alter the answer, given how large the mean is relative to the standard deviation).
Determine whether the finite correction factor should be used. If so, use it in your calculations when you find the probability. In a sample of 100 eruptions of the Old Faithful geyser at Yellowstone National Park, the mean interval between eruptions was 129.58 minutes and the standard deviation was 108.54 minutes. A random sample of size 40 is selected from this population. What is the probability that the mean interval between eruptions is between 119 minutes and 139 minutes? The probability that the mean interval between eruptions is between 119 minutes and 139 minutes is (Round to four decimal places as needed.)
Assume the sample variances to be continuous measurements. Find the probability that a random sample of 31 observations, from a normal population with variance of 6, will have a sample variance between 3.33 and 9,99 Select one: Oa. 0.975 Ob. 0.011 Oc 0.985 Od. 0.965
A population has a mean = 73 and a standard deviation σ = 22. Find the mean and standard deviation of a sampling distribution of sample means with sample size n=240. 1x = (Simplify your answer.)
For a population that has a standard deviation of 22, figure the standard deviation of the distribution of means for samples of size (a)2, (b)4, (c)5 and (d)10.
A population has a mean µ = 87 and a standard deviation o=27. Find the mean and standard deviation of a sampling distribution of sample means with sample size n = 81. (Simplify your answer.)
For all parts of this problem, assume that the weights of tomatoes are normally distributed with a mean of 1.8 lbs and a standard deviation of 0.47 lbs.
A standardized exam's scores are normally distributed. In a recent year, the mean test score was 1458 and the standard deviation was 312. The test scores of four students selected at random are 1860, 1220, 2150, and 1340. Find the z-scores that correspond to each value and determine whether any of the values are unusual. The z-score for 1860 is (Round to two decimal plaes as needed.)
Assume that the readings at freezing on a batch of thermometers are normally distributed with a mean of 0°C and a standard deviation of 1.00°C. A single thermometer is randomly selected and tested. Find P87, the 87-percentile. This is the temperature reading separating the bottom 87% from the top 13%.P87 = °C
Let X represent the full height of a certain species of tree. Assume that X has a normal distribution with a mean of 115.4 ft and a standard deviation of 8.2 ft. A tree of this type grows in my backyard, and it stands 103.9 feet tall. Find the probability that the height of a randomly selected tree is as tall as mine or shorter. My neighbor also has a tree of this type growing in her backyard, but hers stands 119.5 feet tall. Find the nrobability that the ful height of a randomly selected tree is at least as tall as hers. Enter your answers as decimals accurate to 4 decimal places.
The salaries of professional baseball players are heavily skewed right with a mean of $3.2 million and a standard deviation of $2 million. The salaries of professional football players are also heavily skewed right with a mean of $1.9 million and a standard deviation of $1.5 million. A random sample of 40 baseball players' salaries and 35 football players' salaries is selected. The mean salary is determined for both samples. Let -T, represent the difference in the mean salaries for baseball and football players. Which of the following represents the standard deviation of the sampling distribution for - -- ? O 0.41 million O 0,57 million Save and Exit Next Submit Mark this and return hp & 4 6. 7 8. 9. y h k
The weights of people in a certain population are normally distributed with a mean of 159 lb and a standard deviation of 24 lb. Determine the sampling distribution of the mean for samples of size 5.

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