Every day a kindergarten class chooses randomly one of the 50 state flags to hang on the wall, without regard to previous choices, We are interested in the flags that are chosen on Monday, Tuesday and Wednesday of next week.a) Describe a sample space \Omega and a probability measure P to model this experiment.
b) What is the probability that the class hangs Wisconsin's flag on Monday, Michigan's flag on Tuesday, and California's flag on Wednesday.?
c) What is the probability that Wisconsin's flag will be hung at least two of the three days?
Answers
Answer:
a.) P(x = X) =
b.)
c.) 0.00118
Step-by-step explanation:
The sample space Ω = flags of all 50 states
a.) Any one of the flags is randomly chosen. Therefore we can write the
probability measure as P(x = X) = , for all the elements of the sample
space, that is for all x ∈ Ω.
b.) the probability that the class hangs Wisconsin's flag on Monday,
Michigan's flag on Tuesday, and California's flag on Wednesday
=
c.) the probability that Wisconsin's flag will be hung at least two of the three days
= Probability that Wisconsin's flag will be hung on two days + Probability that Wisconsin's flag will be hung on three days
= P(x = 2) + P(x = 3)
=
=
=
= 0.00118
Final answer:
The sample space for this experiment is all the possible combinations of flags from the 50 U.S. states for the three days. The probability of hanging Wisconsin's flag on Monday, Michigan's on Tuesday, and California's on Wednesday is 1/125,000. The probability of hanging Wisconsin's flag at least two of the three days is 294/125,000.
Explanation:
a) The sample space Ω for this experiment comprises of all possible combinations of flags from the 50 U.S. states for the three days. Hence, the total number of outcomes in the sample space Ω would be 50*50*50 = 125,000. Every outcome in this space is equally likely, so the probability measure P would assign a probability of 1/125,000 to each outcome.
b) As each day's choice is independent of the others and each state's flag is equally likely to be chosen, the probability that Wisconsin's flag is hung on Monday, Michigan's flag is hung on Tuesday, and California's flag is hung on Wednesday would be (1/50) * (1/50) * (1/50) = 1/125,000.
c) To find the probability that Wisconsin's flag will be hung at least two of the three days, we have to add the probabilities for the three situations where Wisconsin's flag is hung exactly twice plus the situation where Wisconsin's flag is hung all three days. The final probability would be [(3 * (1/50)² * (49/50)) + (1/50)³] = 294/125,000.
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Answers
Using the sample proportion, it is found that the point estimate is of 0.15 = 15%.
What is a sample proportion?
A sample proportion is given by the number of desired outcomes divided by the number of total outcomes. It can also serve as the point estimate for the population proportion.
In this problem, 12 out of the 80 items sold were returned, hence:
12/80 = 0.15 = 15%.
The point estimate is of 0.15 = 15%.
More can be learned about point estimates at brainly.com/question/24651197
Answer:
a)
b)
And the 95% confidence interval would be given (0.072;0.228).
c) For this case since the confidence interval not contains the value 0.06 or 6% and since the lower limit for the confidence interval is higher than 0.06 (0.072>0.06), we have enough statistical evidence to support the conclusion that the true proportion of items returned is higher than 0.06 or 6% at a significance of 5%.
Step-by-step explanation:
Assumign the following question for the problem:
a. Construct a point estimate of the proportion of items returned for the population of sales transactions at the Houston store.
For this case the best estimate for the true proportion is given by the sample proportion:
b. Construct a 95% confidence interval for the porportion of returns at the Houston store.
A confidence interval is "a range of values that’s likely to include a population value with a certain degree of confidence. It is often expressed a % whereby a population means lies between an upper and lower interval".
The margin of error is the range of values below and above the sample statistic in a confidence interval.
Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".
The confidence interval would be given by this formula
For the 95% confidence interval the value of and
, with that value we can find the quantile required for the interval in the normal standard distribution.
And replacing into the confidence interval formula we got:
And the 95% confidence interval would be given (0.072;0.228).
c. Is the proportion of returns at the Houston store significantly different from the returns for the nation as a whole? Provide statistical support for your answer.
For this case since the confidence interval not contains the value 0.06 or 6% and since the lower limit for the confidence interval is higher than 0.06 (0.072>0.06), we have enough statistical evidence to support the conclusion that the true proportion of items returned is higher than 0.06 or 6% at a significance of 5%.
line.
Answers
Answer:
3 1/2
Step-by-step explanation:
|-7| - |-3 1/2| = 3 1/2
Answers
Answer:
172.12 sq in
Step-by-step explanation:
The figure is comprised of a semicircle, and 2 rectangles
Area of semicircle = 1/2(3.14)4^2 = 25.12
Area of rectangle with length of 9 and width of 7 = 7(9) = 63
Area of rectangle with length of 14 and width of 6 = 6(14) = 84
Total area = 25.12 + 63 + 84 = 172.12 sq in
Answers
Answer:
38.9
Step-by-step explanation:
Answers
$648 is the total amount the customer will pay for the 1-year plan
What is Percentage?
percentage, a relative value indicating hundredth parts of any quantity.
Given that a customer enrolled in a 1-year product purchase plan that costs $60 per month.
After 6 months, the customer received a monthly discount of 20%.
We need to find the total amount the customer will pay for the 1-year plan.
Product Plan = $60 per month
Money he pay for 1 month = $ 60
Money He pay for first 6 month = 6 × 60 = $ 360
after 6 month he receives 20% discount monthly,
So, Now he pay for 1 month = 60 - 20% × 60
=60-20/100×60
=60-12=48
Money he pay for last 6 month = 6 × 48 = 288
Total Money he pay in a year = 360 + 288 = $ 648
Hence, $648 is the total amount the customer will pay for the 1-year plan
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Answer:
$432
Step-by-step explanation:
60*6=360
They paid $360 for the first 6 months.
20%*60=.2*60
0.2*60=12
12*6=72
They paid $72 for the last 6 months.
360+72=432
They paid $432