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Q1. The Bank of Hawaii estimates that 4 percent of credit card holders will be insolvent at some point in their lives. The bank sent 150 new cards today. a) Calculate the expected value (average) of the number of credit card holders who cannot pay their debts? b) Calculate the standard deviation? c) Calculate the probability that all three credit card holders will not pay their debts? d) Calculate the probability that at least one of the credit card holders will not be able to pay their debts? e) Calculate the probability that at most one of the credit card holders will not be able to pay their debts?

Q1. The Bank of Hawaii estimates that 4 percent of credit card holders will be insolvent at some point in their lives. The bank sent 150 new cards today. a) Calculate the expected value (average) of the number of credit card holders who cannot pay their debts? b) Calculate the standard deviation? c) Calculate the probability that all three credit card holders will not pay their debts? d) Calculate the probability that at least one of the credit card holders will not be able to pay their debts? e) Calculate the probability that at most one of the credit card holders will not be able to pay their debts?

MATLAB: An Introduction with Applications
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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Q1. The Bank of Hawaii estimates that 4 percent of credit card holders will be insolvent at some point in their lives. The bank sent 150 new cards today. a) Calculate the expected value (average) of the number of credit card holders who cannot pay their debts? b) Calculate the standard deviation? c) Calculate the probability that all three credit card holders will not pay their debts? d) Calculate the probability that at least one of the credit card holders will not be able to pay their debts? e) Calculate the probability that at most one of the credit card holders will not be able to pay their debts? Q2. The Tool Center has four sales representatives. Below is the number of refrigerators sold in the last month, respectively. Sales Representative Number of Sales Zina Craft 54 Jan Niles 48 Live Junge 50 Molly Camp 50 a) Calculate the mean for each sample, listing all possible binary samples. b) Compare the mean of the sample means with the mean of the population. c) Draw the probability distributions and compare the shape of the population distribution with the distribution of the sample means. Q3. An average of $23.50 per purchase is made by a typical customer at Churchill's Grocery. The standard deviation is $5.00. Suppose the distribution of quantities purchased follows the normal distribution. Answer the following questions for an example of 50 customers. a) What is the probability that the sample mean is at least $25.00? b) What is the probability that the sample mean is between $22.50 and $25.00? c) What limits are within 90 percent of the sample averages? Q4. In a survey of 64 randomly selected iPhone users, it was calculated that the average purchase price was $460 and the standard deviation $120. a) Calculate the 99 percent confidence interval for the sales average. b) What must be the sample size to estimate the mean value of the population with an error of $10?
Transcribed Image Text:Q1. The Bank of Hawaii estimates that 4 percent of credit card holders will be insolvent at some point in their lives. The bank sent 150 new cards today. a) Calculate the expected value (average) of the number of credit card holders who cannot pay their debts? b) Calculate the standard deviation? c) Calculate the probability that all three credit card holders will not pay their debts? d) Calculate the probability that at least one of the credit card holders will not be able to pay their debts? e) Calculate the probability that at most one of the credit card holders will not be able to pay their debts? Q2. The Tool Center has four sales representatives. Below is the number of refrigerators sold in the last month, respectively. Sales Representative Number of Sales Zina Craft 54 Jan Niles 48 Live Junge 50 Molly Camp 50 a) Calculate the mean for each sample, listing all possible binary samples. b) Compare the mean of the sample means with the mean of the population. c) Draw the probability distributions and compare the shape of the population distribution with the distribution of the sample means. Q3. An average of $23.50 per purchase is made by a typical customer at Churchill's Grocery. The standard deviation is $5.00. Suppose the distribution of quantities purchased follows the normal distribution. Answer the following questions for an example of 50 customers. a) What is the probability that the sample mean is at least $25.00? b) What is the probability that the sample mean is between $22.50 and $25.00? c) What limits are within 90 percent of the sample averages? Q4. In a survey of 64 randomly selected iPhone users, it was calculated that the average purchase price was $460 and the standard deviation $120. a) Calculate the 99 percent confidence interval for the sales average. b) What must be the sample size to estimate the mean value of the population with an error of $10?
$1. Bank of Havaii says 4 percent ol credit card holderswill beunable to pay alf debt at some point in their lives predicts it vill. The bank sent 150 new cardstoday. a) Calculate the expected value (average) of the umber of credit card holders who cannot pay their debts? b) Calculate the standard deviation? c) Calculate the probability of three caredit card holders not paying their debts? d) Calculate the probability that at least one of the credit card holders will not be able to pay their debts? e) Calculate the probability of not paying the debt of at most one of the credit card holders? 02. The Tool Center has four sales representatives. Belowis thenumber of refrigerators sold in the last month, respectively given. Sales Reptesentative Number of Sales Zna Craft 54 Jan Niles 48 50 Woon Young Mlly Camp 50 a) Calculate the mesan lor each sample, listing all possitie inary samples. b) Compare the mean of the samplemeans with the mean of the poputation c) Draw the probability distributions and compare the shape of the population distribution with the distribution of the sample msns 53. An average ol $23.50 is shopped by a typical customer at Churchill's Grocery. The standard deviationis $5.00, Thedistributionof quantities purchased follows the normal distribution. let's assime ArWer the following questions for an example of 50 custamers. a) What is the prohalility that the sample mesan is at lesast $25.007 b) What is the prohability that the samplemeanis between $22.50 and $25.00? c) Between vhich nerves are 90 percent of the sampleaverages located? 51. Inasurvey of64randonly selected iPhone users, itvais calculated that the average purchase pricevas SA60 and the standard deviation $120. a) Calculate the 99 percent confdence interval for the sales average. b) What is the number of samples to estimate the mean valtre of the poptilation with an error of $10? shottd it be?
Transcribed Image Text:$1. Bank of Havaii says 4 percent ol credit card holderswill beunable to pay alf debt at some point in their lives predicts it vill. The bank sent 150 new cardstoday. a) Calculate the expected value (average) of the umber of credit card holders who cannot pay their debts? b) Calculate the standard deviation? c) Calculate the probability of three caredit card holders not paying their debts? d) Calculate the probability that at least one of the credit card holders will not be able to pay their debts? e) Calculate the probability of not paying the debt of at most one of the credit card holders? 02. The Tool Center has four sales representatives. Belowis thenumber of refrigerators sold in the last month, respectively given. Sales Reptesentative Number of Sales Zna Craft 54 Jan Niles 48 50 Woon Young Mlly Camp 50 a) Calculate the mesan lor each sample, listing all possitie inary samples. b) Compare the mean of the samplemeans with the mean of the poputation c) Draw the probability distributions and compare the shape of the population distribution with the distribution of the sample msns 53. An average ol $23.50 is shopped by a typical customer at Churchill's Grocery. The standard deviationis $5.00, Thedistributionof quantities purchased follows the normal distribution. let's assime ArWer the following questions for an example of 50 custamers. a) What is the prohalility that the sample mesan is at lesast $25.007 b) What is the prohability that the samplemeanis between $22.50 and $25.00? c) Between vhich nerves are 90 percent of the sampleaverages located? 51. Inasurvey of64randonly selected iPhone users, itvais calculated that the average purchase pricevas SA60 and the standard deviation $120. a) Calculate the 99 percent confdence interval for the sales average. b) What is the number of samples to estimate the mean valtre of the poptilation with an error of $10? shottd it be?
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Since you have asked multiple questions, we will solve the first question for you. If you want any specific question to be solved then please specify the question number or post only that question.

Binomial distribution allows us to compute the probability of observing specified number of events (successes) occurring when the process is repeated a specific number of times and the outcomes would be a success or a failure.

The requirements of the binomial distribution could be specified below:

Each trial should have two possibilities. That is, it should have a success and a failure.
The number of trials in the given experiment must be fixed.
The outcomes of the trials must be independent to each other.
The probabilities of successes and failure must be same for each trail throughout the experiment.

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