The positive integer k has exactly two positive prime factors, 3 and 7. If k has a total of 6 positive factors, including 1 and
1 answer:
Answer:
k is 63
Step-by-step explanation:
The positive integer k has exactly two positive prime factors, 3 and 7
Lets write the combination of prime factors including 1 and k
1, 3, 7, _ , _ , k
using the above factors 3 times 7 is also the factor
so 21 is the other factor
1, 3, 7, 21 , _ , k
Now we use the given statements
(1) 3^2 is a factor, so 9 is also a factor
1, 3, 7, 21 , 9 , k
7^2 is NOT a factor of k. so 49 is not a factor of k
So 3,3 and 7 is the factor of k
K is 63
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Answer:
a)
So the value of height that separates the bottom 75% of data from the top 25% is 236.121.
b)
c)
Step-by-step explanation:
Previous concepts
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 Z-score is "a numerical measurement used in statistics of a value's relationship to the mean (average) of a group of values, measured in terms of standard deviations from the mean".
2) Part a
Let X the random variable that represent the cuts of a population, and for this case we know the distribution for X is given by:
Where and
For this part we want to find a value a, such that we satisfy this condition:
(a)
(b)
Both conditions are equivalent on this case. We can use the z score again in order to find the value a.
As we can see on the figure attached the z value that satisfy the condition with 0.75 of the area on the left and 0.25 of the area on the right it's z=0.674. On this case P(Z<0.674)=0.75 and P(z>0.674)=0.25
If we use condition (b) from previous we have this:
But we know which value of z satisfy the previous equation so then we can do this:
And if we solve for a we got
So the value of height that separates the bottom 75% of data from the top 25% is 236.121.
Part b
For this case we know that the individual probability of select one wheel with a cutting rate higher than the calculated value in part a is 0.25, and we select n =10 so then we can use the binomial distribution for this case:
And we want this probability:
We can find the individual probabilities like this:
Part c
For this case we know that the distribution for the sample mean is given by:
And we want this probability:
And for this case we can use the complement rule and the z score given by:
And if we replace we got: