The probability that a given 20-35 year old survives a given viral infection is 99%. • The probability that a given 65-80 year old survives the same viral infection is 95%. • In a group of 20 20-to-35-year-olds with the viral infection, what is the probability that all 20 will survive? • In a group of 20 65-to-80-year-olds with the infection, what is the probability that all 20 will survive?
In: Statistics and Probability
In: Math
A gender-selection technique is designed to increase the likelihood that a baby will be a girl. In the results of the gender-selection technique,961 births consisted of 501 baby girls and 460 baby boys. In analyzing these results, assume that boys and girls are equally likely.a.
Find the probability of getting exactly 501 girls in 961 births.
b. Find the probability of getting 501 or more girls in 961 births. If boys and girls are equally likely, is 501 girls in 961 births unusually high?
c. Which probability is relevant for trying to determine whether the technique is effective: the result from part (a) or the result from part (b)?
d. Based on the results, does it appear that the gender-selection technique is effective?
a.The probability of getting exactly 501 girls in 961 births is nothing.
(Round to four decimal places as needed.)
b.The probability of getting 501 or more girls in 961 births is nothing.
(Round to four decimal places as needed.)
If boys and girls are equally likely, is 501 girls in 961 births unusually high?
A.No, because 501 girls in 961 births is not far from what is expected, given the probability of having a girl or a boy.
B.No, because 501 girls in 961 births is far from what is expected, given the probability of having a girl or a boy.
C.Yes, because 501 girls in 961 births is not far from what is expected, given the probability of having a girl or a boy.
D.Yes, because 501 girls in 961 births is far from what is expected, given the probability of having a girl or a boy.
c. Which probability is relevant for trying to determine whether the technique is effective, the result from part (a) or the result from part (b)?
A.The result from part (b) is more relevant, because one wants the probability of a result that is at least as extreme as the one obtained.
The result from part (a) is more relevant, because one wants the probability of a result that is exactly equal to the one obtained.
C.
Neither of the results are relevant.
D.
The results from part (a) and part (b) are equal, so they are equally relevant.
d. Based on the results, does it appear that the gender-selection technique is effective?
A.
Yes,because the probability of having 501 or more girls in 961 births i unlikely,and thus,is not attributable to random chance.
B.No, because the probability of having 501 or more girls in 961 births is not unlikely,and thus, is attributable to random chance.
C.
Yes, because the probability of having 501 or more girls in 961 births is not unlikely, and thus,is not attributable to random chance.
D.
No,because the probability of having 501 or more girls in 961 births is not unlikely,and thus,is attributable to random chance.
In: Statistics and Probability
Kay listens to either classical or country music every day while she works. If she listens to classical music one day, there is a 60% chance that she will listen to country music the next day. If she listens to country music, there is a 78% that she will listen to classical music the next day.
(a) If she listens to country music on Monday, what is the
probability she will listen to classical music on Wednesday?
(b) If she listens to classical on Monday, what is the probability
she will listen to classical on Wednesday?
(c) If she listens to classical music on Monday, what is the
probability she will listen to country music on Thursday?
(d) If she listens to country music on Monday, what is the
probability she will listen to country music on Thursday?
All of the same information about Kay's listening habits remain
true. However, suppose you know the additional fact that on a
particular Monday the probability that she is
listening to classical music is 0.38.
(e) Based on your additional knowledge that there is a 0.38
probability that she is listening to classical music on Monday,
what is the probability she will be listening to country music on
Wednesday?
(f) Based on your additional knowledge that there is a 0.38
probability that she is listening to classical music on Monday,
what is the probability that she will be listening to classical
music on Thursday?
In: Statistics and Probability
1. Approximately 25% of the adult population is allergic to pets with fur or feathers, but only 4% of the adult population has a food allergy. A quarter of those with food allergies also have pet allergies.What is the probability a person has food allergies but is not allergic to pets?
A. 0.01
B. 0.03
C. 0.04
D. 0.0625
E. 0.24
2. Suppose the probability there are children in a car involved in an auto accident is 0.3. Further suppose that if there are children in a car that is involved in an auto accident, there is a 0.1 probability the driver was 55 years or older. However, if there no children in a car that is involve in an auto accident, suppose there is a 0.25 probability that driver was 55 years or older.What is the probability there were children in a car involved in an auto accident if the driver was not 55 years or older?
A. 0.66
B. 0.34
C. 0.333
D. 0.27
E. 0.01
3. Suppose the probability there are children in a car involved in an auto accident is 0.3. Further suppose that if there are children in a car that is involved in an auto accident, there is a 0.1 probability the driver was 55 years or older. However, if there no children in a car that is involve in an auto accident, suppose there is a 0.25 probability that driver was 55 years or older.What is the probability there were no children in a car involved in an auto accident if the driver was not 55 years or older?
A. 0.933
B. 0.66
C. 0.525
D. 0.34
E. 0.25
In: Statistics and Probability
Let us assume that from a population with mean ?=100 and
standard deviation ?=15 a sample random variable of ?=900 is
selected.
a. What is the probability ?(?̅<101.1)?
b. What is the probability ?(?̅>101.5)?
c. What is the probability ?(99.3<?̅<100.5)?
In: Statistics and Probability
If you have a 52 card deck:
A) What is the probability of selecting 2 kings from the deck?
B) What is the probability of selecting 3 queens?
C) What is the probability of selecting a king, and then an ace, and then a ten?
Thank you.
In: Statistics and Probability
Suppose a die is rolled six times and you need to find
a) The probability that at least two 4 come up
b) The probability that at least five 4's come up
Solve using the Binomial probability formula.
In: Math
Monte Carlo Simulation
Tully Tyres sells cheap imported tyres. The manager believes its profits are in decline. You have just been hired as an analyst by the manager of Tully Tyres to investigate the expected profit over the next 12 months based on current data.
•Monthly demand varies from 100 to 200 tyres – probabilities
shown in the partial section of the spreadsheet below, but you have
to insert formulas to ge the cumulative probability distribution
which can be used in Excel with the VLOOKUP command.
•The average selling price per tyre follows a discrete uniform
distribution ranging from $160 to $180 each. This means that it can
take on equally likely integer values between $160 and $180 – more
on this below.
•The average profit margin per tyre after covering variable costs
follows a continuous uniform distribution between 20% and 30% of
the selling price.
•Fixed costs per month are $2000.
(a)Using Excel set up a model to simulate the next 12 months to determine the expected average monthly profit for the year. You need to have loaded the Analysis Toolpak Add-In to your version of Excel. You must keep the data separate from the model. The model should show only formulas, no numbers whatsoever except for the month number.
You can use this partial template to guide you:
| Tully Tyres | |||||||
| Data | |||||||
| Probability | Cumulative probability | Demand | Selling price | $160 | $180 | ||
| 0.05 | 100 | Monthly fixed cost | $2000 | ||||
| 0.1 | 120 | Profit margin | 20% | 30% | |||
| 0.2 | 140 | ||||||
| 0.3 | 160 | ||||||
| 0.25 | 180 | ||||||
| 0.1 | 200 | ||||||
| 1 | |||||||
| Model | |||||||
| Month | Random number1 | Demand | Selling price | Random number 2 | Profit margin | Fixed cost | Profit |
| 1 | 0.23297 | #N/A | $180 | 0.227625 | 0.2 | ||
The first random number (RN 1) is to simulate monthly demands
for tyres.
•The average selling price follows a discrete uniform distribution
and can be determined by the function =RANDBETWEEN(160,180) in this
case. But of course you will not enter (160,180) but the data cell
references where they are recorded.
•The second random number (RN 2) is used to help simulate the
profit margin.
•The average profit margin follows a continuous uniform
distribution ranging between 20% and 30% and can be determined by
the formula =0.2+(0.3-0.2)*the second random number (RN 2). Again
you do not enter 0.2 and 0.3 but the data cell references where
they are located. Note that if the random number is high, say 1,
then 0.3-0.2 becomes 1 and when added to 0.2 it becomes 0.3. If the
random number is low, say 0, then 0.3-0.2 becomes zero and the
profit margin becomes 0.2.
•Add the 12 monthly profit figures and then find the average
monthly profit.
Show the data and the model in two printouts: (1) the results, and (2) the formulas. Both printouts must show the grid (ie., row and column numbers) and be copied from Excel and pasted into Word. See Spreadsheet Advice in Interact Resources for guidance.
(b)Provide the average monthly profit to Tully Tyres over the 12-month period.
(c)You present your findings to the manager of Ajax Tyres. He thinks that with market forces he can increase the average selling price by $40 (ie from $200 to $220) without losing sales. However he does suggest that the profit margin would then increase from 22% to 32%.
He has suggested that you examine the effect of these changes and report the results to him. Change the data accordingly in your model to make the changes and paste the output in your Word answer then write a report to the manager explaining your conclusions with respect to his suggestions. Also mention any reservations you might have about the change in selling prices.
The report must be dated, addressed to the Manager and signed
off by you.
(Word limit: No more than 150 words)
In: Math
Peter Andrus owned an apartment building that he had insured under a fire insurance policy sold b... Peter Andrus owned an apartment building that he had insured under a fire insurance policy sold by J.C. Durick Insurance (Durick). Two months prior to the expiration of the policy, Durick notified Andrus that the building should be insured for $48,000 (or 80 percent of the building’s value), as required by the insurance company. Andrus replied that (1) he wanted insurance to match the amount of the outstanding mortgage on the building (i.e., $24,000) and (2) if Durick could not sell this insurance, he would go elsewhere. Durick sent a new insurance policy in the face amount of $48,000 with the notation that the policy was automatically accepted unless Andrus notified him to the contrary. Andrus did not reply. However, he did not pay the premiums on the policy. Durick sued Andrus to recover these premiums.
Who wins?
In: Accounting