A circle has its centre at (0,0) and passes through the point (-9,40).
1 answer:
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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
Answer:
So then the confidence interval for the difference of means is given by:
Step-by-step explanation:
Previous concepts
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".
represent the mean for the age of grandmother
represent the mean for the age of grandfather
represent the sample deviation for the age of grandmother
represent the sample deviation for the age of grandfather
Solution to the problem
For this case the confidence interval is given by:
In order to calculate the critical value we need to find first the degrees of freedom, given by:
Since the Confidence is 0.95 or 95%, the value of and
, and we can use excel, a calculator or a table to find the critical value. The excel command would be: "=-T.INV(0.025,18)".And we see that
And replacing we got:
So then the confidence interval for the difference of means is given by: