17 is what percentage of 58?(answers rounded to the nearest whole number percent)
2 answers:
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Answer:
The correct option is 1 - [(0.8)¹⁰+10*0.2*(0.8)⁹]= 0.6242
Step-by-step explanation:
Hello!
Given the distribution of probabilities for blood types for African-Americans:
O: 0.4
A: 0.2
B: 0.32
AB: 0.08
A random sample of 10 African-American is chosen, what is the probability that 2 or more of them have Type A blood?
Let X represent "Number of African-Americans with Type A blood in a sample of 10.
Then you have two possible outcomes,
"Success" the person selected has Type A blood, with an associated probability p= 0.2
"Failure" the selected person doesn't have Type A blood, with an associated probability q= 0.8
(You can calculate it as "1-p" or adding all associated probabilities of the remaining blood types: 0.4+0.32+0.08)
Considering, that there is a fixed number of trials n=10, with only two possible outcomes: success and failure. Each experimental unit is independent of the rest and the probability of success remains constant p=0.2, you can say that this variable has a Binomial distribution:
X~Bi(n;p)
You can symbolize the asked probability as:
P(X≥2)
This expression includes the probabilities: X=2, X=3, X=4, X=5, X=6, X=7, X=8, X=9, X=10
And it's equal to
1 - P(X<2)
Where only the probabilities of X=0 and X=1 are included.
There are two ways of calculating this probability:
1) Using the formula:
With this formula, you can calculate the point probability for each value of X=x₀ ∀ x₀=1, 2, 3, 4, 5, 6, 7, 8, 9, 10
So to reach the asked probability you can:
a) Calculate all probabilities included in the expression and add them:
P(X≥2)= P(X=2) + P(X=3) + P(X=4) + P(X=5) + P(X=6) + P(X=7) + P(X=8) + P(X=9) + X=10
b) Use the complement rule and calculate only two probabilities:
1 - P(X<2)= 1 - [P(X=0)+P(X=1)]
2) Using the tables of the binomial distribution.
These tables have the cumulative probabilities listed for n: P(X≤x₀)
Using the number of trials, the probability of success, and the expected value of X you can directly attain the corresponding cumulative probability without making any calculations.
>Since you are allowed to use the complement rule I'll show you how to calculate the probability using the formula:
P(X≥2) = 1 - P(X<2)= 1 - [P(X=0)+P(X=1)] ⇒
⇒ 1 - (0.1074+0.2684)= 0.6242
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Using the table:
P(X≥2) = 1 - P(X<2)= 1 - P(X≤1)
You look in the corresponding table of n=10 p=0.2 for P(X≤1)= 0.3758
1 - P(X≤1)= 1 - 0.3758= 0.6242
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Full text in attachment.
I hope it helps!
Answer:
(a) Correct option (1).
(b) Correct option (3).
(c) Correct option (2).
Step-by-step explanation:
A one-sample <em>z</em>-test for mean is used to determine whether the claimed value of mean is significant or not. To perform this test we can also use the <em>t</em>-distribution.
The <em>t</em>-test is used if the following conditions are given:
- The population is normally distributed
- The population standard deviation is not known
- The sample selected is large enough.
Similarly the (1 - <em>α</em>)% confidence interval for population mean can be computed either using the <em>z</em>-interval or the <em>t</em>-interval.
The same conditions should be applied to use the <em>t</em>-interval.
(a)
In the first case, Gale wants to determine the likely range of weight of whole coffee beans from her trusty two-tablespoon scoop to create a reliable method of brewing the perfect cup of coffee.
She selects a sample of <em>n</em> = 15 scoops and perform the test.
Since the population standard deviation is not known and Gale wants to know the range of weight of whole coffee beans , she should use a one sample <em>t</em>-confidence interval for a mean.
The correct option is (1).
(b)
In the second case, Tanya wants to determine whether the mean IQ score is at least 112 or not.
She selects a a random sample <em>n</em> = 20 composers and compute the statistic to perform the one-sample test.
Since the population standard deviation is not known, Tanya should use one sample t-test for a mean.
The correct option is (3).
(c)
In the second case, Jason wants to estimate what the balance of his retirement account will be in one month.
He selects the data from 1950 to 2015 and calculates this index has had an average monthly return of 0.69% with a standard deviation of 4.15%.
Now, the sample selected is quite large. The Central limit theorem can be used to approximate the sampling distribution of sample mean.
Then,
So, Jason can use the one sample z-test for a mean to determine the balance of his retirement account will be in one month.
The correct option is (2).
Answer:
B) Owen can have a maximum of 22 rabbits in the store.
Step-by-step explanation:
Consider:
"He wants to ensure he has more than 1 pound of dry food for every four rabbits he has in the store."
It means, at least 0.25 pounds per rabbit. (1 pound divided by four)
"He currently has 5.7 pounds of dry food."
Inequality (r is the number of rabbits):
According to the inequality, he can only have a maximum of 22 rabbits.