2. Let X be a random variable that represents the weights, in pounds, of Alaska King Salmon. Assume that X follows anormal distribution with mu = 30 and sigma = 10. (Practice using the table in the book and then verify usingtechnology.)a. Find the probability that a randomly selected Salmon weighs less than 25 pounds.b. Find the weight in pounds such that only 10% of Salmon weigh more than that.

Answered: 2. Let X be a random variable that…

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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Scores on the Wechsler Adult Intelligence Scale are approximately normally distributed with 100 and σ=15. Use Table B or software to answer the following questions. What scores fall in the lowest 25% of the distribution? How high a score is needed to be in the highest 5%?
Sports shirts are frequently classified as S, M, L, XL for small, medium, large and extra-large neck sizes. S fits a neck circumference of less than 37cm, M fits between 37 and 40.5cm and L fits between 40.5cm and 44cm while XL fits necks over 44cm in circumference. The neck circumference of adult males has a normal distribution with µ = 40cm and σ = 2cm. (i) What proportion of shirts should be manufactured in each category? (ii) If you wanted to define categories S, M, L, XL so that the categories con- tained 20%, 30%, 30% and 20% respectively, of the total population of adult males, what neck sizes must you assign to each of the categories?
The Normal model N(150,10) describes the distribution of scores on the LSAT, a standardized test required by most law schools. Which of the following questions asks for a probability, and which asks for a measurement? Identify the type of problem and then answer the given question. a. A law school applicant scored at the 60th percentile on the LSAT. What was the applicant's LSAT score? b. A law school applicant scored 164 on the LSAT. This applicant scored higher than what percentage of LSAT test takers? a. Identify the type of problem. Statement a asks for a What was the applicant's LSAT score? (Round to the nearest integer as needed.) b. Identify the type of problem. Statement b asks for a This applicant scored higher than what percentage of LSAT test takers? |% (Round to the nearest integer as needed.)
PROBLEM 4. Charles claims that he can distinguish between beer and ale 75 percent of the time. Ruth bets that he cannot and, in fact, just guesses. To settle this, a bet is made: Charles is to be given ten small glasses, each having been filled with beer or ale, chosen by tossing a fair coin. He wins the bet if he gets seven or more correct. Find the probability that Charles wins if he has the ability that he claims. Find the probability that Ruth wins if Charles is guessing.
A scientist claims that pneumonia causes weight loss in mice. The table shows the weights (in grams) of six mice before infection and two days after infection. At a=0.10, is there enough evidence to support the scientist's claim? Assume the samples are random and dependent, and the population is normally distributed. Complete parts (a) through (e) below. Mouse Weight (before) Welght (after) 1 2 3 4 5 22.7 21.6 20.6 20.6 21.7 22.9 21.3 20.9 19.9 20.2 20.6 21.7 H: >0 O D. Ho: H20 OE Ho: H0 OF. Ha: H zd 0> PH :"H (b) Find the critical value(s) and identify the rejection region(s). Select the correct choice below and fill in any answer boxes to complete your choice. (Round to three decimal places as needed.) OA. te B. t> 1476 OC. t (c) Calculate d and s d= 0.917 (Round to three decimal places as needed.) Calculate sg S= 0.376 (Round to three decimal places as needed.) (d) Find the standardized test statistic t. t= (Round to three decimal places as needed.)
Gentle Ben is a Morgan horse at a Colorado dude ranch. Over the past 8 weeks, a veterinarian took the following glucose readings from this horse (in mg/100 ml). 95 88 80 107 101 108 84 87 The sample mean is x ≈ 93.8. Let x be a random variable representing glucose readings taken from Gentle Ben. We may assume that x has a normal distribution, and we know from past experience that ? = 12.5. The mean glucose level for horses should be ? = 85 mg/100 ml.† Do these data indicate that Gentle Ben has an overall average glucose level higher than 85? Use ? = 0.05. (a) Compute the z value of the sample statistic. (Round your answer to two decimal places.) (b) Find (or estimate) the P-value. (Round your answer to four decimal places.)
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We learned that there are 4 items by which we characterize a distribution in statistics. Which of the followings is NOT one of them? O a. Central tendency Ob. Homogeneity O c. Skewness Od. Kurtosis
Gentle Ben is a Morgan horse at a Colorado dude ranch. Over the past 8 weeks, a veterinarian took the following glucose reading from the horse (in mg/100 mg). 92 87 82 107 99 109 85 89 The sample mean x-bar is 93.8. Let x be a random variable representing glucose readings taken from gentle Ben. We may assume x has a normal distribution, and we know from past experience that the standard deviation = 12.5. The mean glucose level for horses should be mu = 85mg/100gl. Do these data indicate that gentle Ben have a overall average glucose level higher than 85? Use alpha = 0.05 A- Compute z value of the sample stasistic test. Round answer to 2 decimal places B- Find (or estimte) the P-Value . Round answer to 4 decimal places I get 1.99 for the z value but cannot come up with correct p-value.
D. Tell whether the distribution has a small or large variance E. Compute the actual variance and standard deviation
Using the data attached, compute x-bar: 1. Define the random variable x-bar in words 2. state the estimated distribution to use. Use both words and symbols.
6. Suppose that the distance of fly balls hit to the outfield (in baseball) is normally distributed with a mean of 210 feet and a standard deviation of 50 feet. Let X = distance in feet for a fly ball. Write the probability statement. (Let k represent the score that corresponds to the 80th percentile.) 80th percentile: 252.1 ft

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