The sum of three consecutive multiples of 3 is equal to 6 more than four times the smallest multiple. What is the largest multip
2 answers:
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Answer:
90.67% probability that John finds less than 7 golden sheets of paper
Step-by-step explanation:
For each container, there are only two possible outcomes. Either it contains a golden sheet of paper, or it does not. The probability of a container containing a golden sheet of paper is independent of other containers. So we use the binomial probability distribution to solve this question.
Binomial probability distribution
The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.
In which is the number of different combinations of x objects from a set of n elements, given by the following formula.
And p is the probability of X happening.
At Munder Difflin Paper Company, the manager Mitchell Short randomly places golden sheets of paper inside of 30% of their paper containers.
This means that
14 of these containers of paper.
This means that
What is the probability that John finds less than 7 golden sheets of paper?
In which
90.67% probability that John finds less than 7 golden sheets of paper
The first part of the question is missing and it says;
Use these parameters: Men's heights are normally distributed with mean 68.6 in. and standard deviation 2.8 in. Women's heights are normally distributed with mean 63.7 in. and standard deviation 2.9 in.
Answer:
A) Percentage of women meeting the height requirement = 72.24%
B) Percentage of men meeting the height requirement = 0.875%
C) Corresponding women's height =67.42 inches while corresponding men's height = 72.19 inches
Step-by-step explanation:
From the question,
For men;
Mean μ = 68.6 in
Standard deviation σ = 2.8 in
For women;
Mean μ = 63.7 in
Standard deviation σ = 2.9 in
Now let's calculate the standardized scores;
The formula is z = (x - μ)/σ
A) For women;
Z = (62 - 63.7)/2.9 = - 0.59
Z = (78 - 63.7)/2.9 = 4.93
The original question cam be framed as;
P(62 < X < 78).
So thus, the probability of only women will take the form of;
P(-0.59 < Z < 4.93) = P(Z<4.93) - P(Z > - 0.59)
From the normal probability table attached, when we interpolate, we'll arrive at P(Z<4.93) = 0.9999996
And P(Z > - 0.59) = 0.277595
Thus;
P(Z<4.93) - P(Z > - 0.59) =0.9999996 - 0.277595 = 0.7224
So, percentage of women meeting the height requirement is 72.24%.
B) For men;
Z = (62 - 68.6)/2.8 = -2.36
Z = (78 - 68.6)/2.8 = 3.36
Thus, the probability of only men will take the form of;
P(-2.36 < Z < 3.36) = P(Z<3.36) - P(Z > - 2.36)
From the normal probability table attached, when we interpolate, we'll arrive at P(Z<3.36) = 0.99961
And P(Z > -2.36) = 0.99086
Thus;
P(Z<3.36) - P(Z > -2.36) 0.99961 - 0.99086 = 0.00875
So, percentage of women meeting the height requirement is 72.24%.
B)For women;
Z = (62 - 63.7)/2.9 = - 0.59
Z = (78 - 63.7)/2.9 = 4.93
The original question cam be framed as;
P(62 < X < 78).
So thus, the probability of only women will take the form of;
P(-0.59 < Z < 4.93) = P(Z<4.93) - P(Z > - 0.59)
From the normal probability table attached, when we interpolate, we'll arrive at P(Z<4.93) = 0.9999996
And P(Z > - 0.59) = 0.277595
Thus;
P(Z<4.93) - P(Z > - 0.59) =0.9999996 - 0.277595 = 0.00875
So, percentage of women meeting the height requirement is 0.875%
C) Since the height requirements are changed to exclude the tallest 10% of men and the shortest10% of women.
For women;
Let's find the z-value with a right-tail of 10%. From the second table i attached ;
invNorm(0.90) = 1.2816
Thus, the corresponding women's height:: x = (1.2816 x 2.9) + 63.7= 67.42 inches
For men;
We have seen that,
invNorm(0.90) = 1.2816
Thus ;
Thus, the corresponding men's height:: x = (1.2816 x 2.8) + 68.6 = 72.19 inches
