Sofia tosses 4 coins a total of 80 times. The following table shows the distribution of the number of heads obtainedin each toss of 4 coins.Number of14.headsFrequency10242617a. Using the binomial distribution B(4, 0.5) find the expected probabilities of obtaining 0,1,2,3 or 4 headsrespectivelyb. Perform a goodness of fit test at the 5% significance level to find out whether the data fits a binomialdistribution. State the null and alternative hypotheses and justify any conclusions found. The critical valuefor this test is 6.64.3.2.

Let X denotes the number of heads X ~B(4,0.5) The Binomial probability formula is :

Answered: Sofia tosses 4 coins a total of 80…

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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Aleks spins a 9 sided spinner 56 times. Each of the nine sides has a different colour on it. He records the number of times that he spins the colour purple. Is it reasonable to approximate this distribution with a normal distribution? Give a reason.
Talent Corp is a HR-consulting firm. The number of new clients that they have obtained each month has ranged from 0 to 6. The number of new clients has the probability distribution that is shown below. Number of New Clients Probability 0 0.05 1 0.10 2 0.15 3 0.30 4 0.25 5 0.10 6 0.05 Compute the expected number of new clients each month. Compute the variance and standard deviation for the expected number of new clients. What is the probability that there will be 2 or fewer clients next month?
A researcher wanted to determine if carpeted or uncarpeted rooms contain more bacteria. The table shows the results for the number of bacteria per cubic foot for both types of rooms. A normal probability plot and boxplot indicate that the data are approximately normally distributed with no outliers. Do carpeted rooms have more bacteria than uncarpeted rooms at the a = 0.01 level of significance? Full data set O Carpeted 14.3 9.8 10.7 12.2 Uncarpeted 9.5 9.5 10.9 2.1 15 3 15.8 5.4 6.4 15.2 4.3 10.6 - X Student t-distribution Area in right tail t-Distribution Area in Right Tail Degrees of Freedom 0.25 0.20 0.15 0.10 0.05 0.025 0.02 0.01 0.005 0.0025 0.001 0.0005 1.000 0.816 0.765 0.741 1.376 1.061 0.978 0.941 0.920 1.963 1.386 1.250 1.190 1.156 3.078 1.886 1.638 1.533 6.314 2.920 2.353 2.132 12.706 4.303 3.182 2.776 2.571 15.894 4.849 3.482 2.999 2.757 31.821 6.965 4.541 3.747 3.365 63.657 9.925 5.841 4.604 4.032 127.32 1 14.089 7453 5.598 318.309 636.619 31.599 12.924 8.610 6.869 22.327…
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Q6
A racing car consumes a mean of 100 gallons of gas per race with a variance of 64. If 44 racing cars are randomly selected, what is the probability that the sample mean would be greater than 98.8 gallons? Round your answer to four decimal places. Answer How to enter your answer (opens in new window) Statistical Tables Binomial Probabilities Binomial Cumulative ▾ Poisson Probabilities Poisson Cumulative Tables Keypad Keyboard Shortcuts Binomial Probabilities (n=1) Probability of Success or p 0.4 0.5 X 0.3 0.1 0.2 0.6 0 0.9000 0.8000 0.7000 0.6000 0.5000 0.4000 0.7 0.8 0.9 0.3000 0.2000 0.1000 1 0.1000 0.2000 0.3000 0.4000 0.5000 0.6000 0.7000 0.8000 0.9000 X

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