A researcher studied the relationship between the salary of a working woman with school-aged children and the number of children she had. The results are shown in the following frequency table:

                                             Number of Children

         If a working woman has more than 2 children, what is the probability she has a low or medium salary?

         A.      0.79            B.      0.45            C.      0.35            D.      0.95

Banner Mattress and Furniture Company wishes to study the number of credit applications received per day for the last 395 days.

The sample information is reported below.

To interpret, there were 10 days on which no credit applications were received, 26 days on which only one application was received, and so on. Would it be reasonable to conclude that the population distribution is Poisson with a mean of 4.0? Use the 0.1 significance level. Hint: To find the expected frequencies use the Poisson distribution with a mean of 4.0. Find the probability of exactly one success given a Poisson distribution with a mean of 4.0. Multiply this probability by 395 to find the expected frequency for the number of days in which there was exactly one application. Determine the expected frequency for the other days in a similar manner.

H₀: Distribution with Poisson with µ = 4.

H₁: Distribution is not Poisson with µ = 4.

State the decision rule. Use 0.1 significance level. (Round your answer to 3 decimal places.)

Compute the value of chi-square. (Round f_e to 4 decimal places. Round (f_o - f_e)²/f_e) to 4 decimal places. Round χ² to 4 decimal places.)

What is your decision regarding H₀?

A) A company that owns a large number of grocery stores claims that customers who pay by personal check spend an average of $87 with a standard deviation of $22. Assume the amount spent by these customers is normally distributed.

What is the probability that a customer using a check spends less than $90?

Express your answer as a decimal rounded to four places after the decimal point.

B)

A company that owns a large number of grocery stores claims that customers who pay by personal check spend an average of $87 with a standard deviation of $22. Assume the amount spent by these customers is normally distributed.

What is the probability that a customer using a check spends between $80 and $85?

Express your answer as a decimal rounded to four places after the decimal point.

C)

A company that owns a large number of grocery stores claims that customers who pay by personal check spend an average of $87 with a standard deviation of $22. Assume the amount spent by these customers is normally distributed.

The top 10% of customers using a check pay _____________ or more for groceries.

Round your answer to 2 decimal places.

D)

A company that owns a large number of grocery stores claims that customers who pay by personal check spend an average of $87 with a standard deviation of $22. Assume the amount spent by these customers is normally distributed.

The most frugal 20% of customers pay ___________ or less for groceries.

Round your answer to the nearest hundredth.

1. With the virus outbreak, the average number of times Justin washes his hands during the day is 14 with a standard deviation of 3. Assuming that this number is normally distributed, what is the probability that tomorrow he will wash her hands between 16 and 22 times? Use the z-table to answer the question (Select the answer that is closest to the answer that you calculated.)

   		0.33
   		0.79
   		0.95
   		0.5
   		0.67

2. The mean age of presidents at inauguration is 55 years. The age of presidents at inauguration is normally distributed with a standard deviation of 6.6 years. Donald Trump was 70 years old when he was inaugurated. What proportion of presidents were younger than Donald Trump at their inauguration? Use the z-table to answer this question (Select the answer that is closest to the answer that you calculated.)

   		2.273
   		0.988
   		0.012
   		0.786
   		None of the above

3. Use this information to answer the following two questions: Varshini wants to read 4 books this month, but her busy work schedule may get in the way of her goal. Let X represent the number of books she will read this month. The table below shows the probabilities associated with the number of books she will read this month.

   X	P(X = x)
   0	0.17
   1	0.23
   2
   3	0.32
   4	0.16

   What is the probability that she reads less than 3 books?

   		0.48
   		0.52
   		0.84
   		0.74
   		This cannot be determined based on the data provided.

A random sample of 40 adults with no children under the age of 18 years results in a mean daily leisure time of 5.83 ​hours, with a standard deviation of 2.49 hours. A random sample of 40 adults with children under the age of 18 results in a mean daily leisure time of 4.47 ​hours, with a standard deviation of 1.89 hours. Construct and interpret a 95​% confidence interval for the mean difference in leisure time between adults with no children and adults with children (mu 1 - mu 2)

Let mu 1μ1 represent the mean leisure hours of adults with no children under the age of 18 and mu 2μ2

represent the mean leisure hours of adults with children under the age of 18.

The 95​% confidence interval for left parenthesis mu 1 minus mu 2 right parenthesisμ1−μ2 is the range from   

hours to hours.

​(Round to two decimal places as​ needed.)

What is the interpretation of this confidence​ interval?

A.There is 95​% confidence that the difference of the means is in the interval. Conclude that there is insufficient evidence of ainsufficient evidence of asignificant difference in the number of leisure hours.

B.There is a 95​%probability that the difference of the means is in the interval. Conclude that there is a significant difference in the number of leisure hours.

C.There is 95​% confidence that the difference of the means is in the interval. Conclude that there is a significant difference in the number of leisure hours.

D. There is an 95​%probability that the difference of the means is in the interval. Conclude that there is insufficient evidence of a significant difference in the number of leisure hours.

I need 7-8 sentences responding to each paragraph written by my peers. Please make sure each paragraph is error/grammar free. Please separate each paragraph written by number 1 and 2. Thanks, Chegg

1- The financial crisis in the United States in 2008-09 was caused by a lack of understanding of probability. Do you think this statement is correct? Why or why not? Please find evidence to support your argument.The statement is correct. Work in risk management has produced a large number of Nobel winners. Sometimes it feels when markets drop the chances of this happening was zero to begin with. No risk management model covers all conceivable possibilities. Social sciences are often based on probabilities.

Here is what happened in the crisis. The money to investors comes from homeowners and if people defaulted less money would flow to the banks and thus the investors. The investment banks put all of the mortgages into a box and called it collateralized debt obligations (CDO's). These packages were sold to others like hedge funds and banks. Some of the mortgages were not very risky but other were subprime. This is were the probability comes in.

The reality is that the banks underwrote very risky assets and insured them with credit default swaps. Underlying these are statistics and probability. The banks predicted that the mortgages, which had been split into solid, okay, and very risky divisions, would stay mostly intact and could gain a AAA credit rating. The small probability that some would go under was a bearable risk. These were going to be insured directly through banks. Otherwise the banks could be sold on the market for ever increasing house prices. The probability that default would happen was in fact much higher than thought. The expected negative return per default situation turned out to be very high. The probability is not constant, that is, it changes over time and is not homogeneous. As more people defaulted more houses went on the market. The more supply the less value to the house. The less market value the less willing people were to pay because they became underwater. This resulted in a reflexive feedback loop increasing the probability of default. In summary, a lack of understanding of probability caused the 2008-2009 financial crisis here in the United States.

2-I think it is correct. Since Fannie Mae and Freddie Mac of government-sponsored mortgages provide loans to borrowers with lower credit scores, the risk of default on such loans is high, so the possibility of these borrowers not repaying the loan is ignored. The root cause is the excessive expansion of housing loans and the lack of strict risk control; excessive innovation in financial products, a large number of structured products that are too complex, difficult to accurately estimate, and risk opaque; financial institutions have excessive leverage and defects in risk management models; financial supervision systems are not Perfect, uncoordinated, inadequate supervision, and not strict accountability; insufficient due diligence of intermediaries, deviations in financial audit and credit rating; excessive incentives and high salaries of financial institutions, which can easily stimulate managers to take risks and pursue profits; for financial institutions and the financial sector Insufficient understanding of the problem contagion and the systemic risks that may arise, and weak monitoring and management. I think that if the government, lenders, and financial institutions have a certain understanding of the probability of default, this will minimize the probability of default.

A survey of 2645 consumers by DDB Needham Worldwide of Chicago for public relations agency Porter/Novelli showed that how a company handles a crisis when at fault is one of the top influences in consumer buying decisions,with 73% claiming it is an influence. Quality of product was the number one influence, with 96% of consumers stating that quality influences their buying decisions. How a company handles complaints was number two, with 85% of consumers reporting it as an influence in their buying decisions. Suppose a random sample of 1,100 consumers is taken and each is asked which of these three factors influence their buying decisions.

a. What is the probability that more than 820 consumers claim that how a company handles a crisis when at fault is an influence in their buying decisions? *

b. What is the probability that fewer than 1,030 consumers claim that quality of product is an influence in their buying decisions? **

c. What is the probability that between 81% and 83% of consumers claim that how a company handles complaints is an influence in their buying decisions? *

*(Round the values of z to 2 decimal places. Round the intermediate values to 4 decimal places. Round your answer to 4 decimal places.) **(Round the values of z to 2 decimal places. Round the intermediate values to 4 decimal places. Round your answer to 5 decimal places.)

Let x be a random variable that represents the weights in kilograms (kg) of healthy adult female deer (does) in December in a national park. Then x has a distribution that is approximately normal with mean μ = 70.0 kg and standard deviation σ = 7.3 kg. Suppose a doe that weighs less than 61 kg is considered undernourished.

(a) What is the probability that a single doe captured (weighed and released) at random in December is undernourished? (Round your answer to four decimal places.)


(b) If the park has about 2650 does, what number do you expect to be undernourished in December? (Round your answer to the nearest whole number.)
does

(c) To estimate the health of the December doe population, park rangers use the rule that the average weight of n = 45 does should be more than 67 kg. If the average weight is less than 67 kg, it is thought that the entire population of does might be undernourished. What is the probability that the average weight

x

for a random sample of 45 does is less than 67 kg (assuming a healthy population)? (Round your answer to four decimal places.)


(d) Compute the probability that

x

< 71.2 kg for 45 does (assume a healthy population). (Round your answer to four decimal places.)

Let x be a random variable that represents the weights in kilograms (kg) of healthy adult female deer (does) in December in a national park. Then x has a distribution that is approximately normal with mean μ = 60.0 kg and standard deviation σ = 8.4 kg. Suppose a doe that weighs less than 51 kg is considered undernourished.

(a) What is the probability that a single doe captured (weighed and released) at random in December is undernourished? (Round your answer to four decimal places.)

(b) If the park has about 2350 does, what number do you expect to be undernourished in December? (Round your answer to the nearest whole number.)

(c) To estimate the health of the December doe population, park rangers use the rule that the average weight of n = 50 does should be more than 57 kg. If the average weight is less than 57 kg, it is thought that the entire population of does might be undernourished. What is the probability that the average weight x for a random sample of 50 does is less than 57 kg (assuming a healthy population)? (Round your answer to four decimal places.)

(d) Compute the probability that x < 61.2 kg for 50 does (assume a healthy population). (Round your answer to four decimal places.)