A school has 240 students. The ratio girls : boys = 25 : 23. Find the number of boys
2 answers:
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Answer:
a) By the Central Limit Theorem, approximately normally distributed, with mean 26 and standard error 0.44.
b) s = 0.44
c) 0.84% of the sample means will be greater than 27.05 seconds
d) 98.46% of the sample means will be greater than 25.05 seconds
e) 97.62% of the sample means will be greater than 25.05 but less than 27.05 seconds
Step-by-step explanation:
To solve this question, we need to understand the normal probability distribution and the central limit theorem.
Normal probability distribution
Problems of normally distributed samples are solved using the z-score formula.
In a set with mean and standard deviation
, the zscore of a measure X is given by:
The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.
Central Limit Theorem
The Central Limit Theorem estabilishes that, for a normally distributed random variable X, with mean and standard deviation
, the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean
and standard deviation(also called standard error)
.
For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.
In this problem, we have that:
a. What can we say about the shape of the distribution of the sample mean time?
By the Central Limit Theorem, approximately normally distributed, with mean 26 and standard error 0.44.
b. What is the standard error of the mean time? (Round your answer to 2 decimal places)
c. What percent of the sample means will be greater than 27.05 seconds?
This is 1 subtracted by the pvalue of Z when X = 27.05. So
By the Central Limit Theorem
has a pvalue of 0.9916
1 - 0.9916 = 0.0084
0.84% of the sample means will be greater than 27.05 seconds
d. What percent of the sample means will be greater than 25.05 seconds?
This is 1 subtracted by the pvalue of Z when X = 25.05. So
has a pvalue of 0.0154
1 - 0.0154 = 0.9846
98.46% of the sample means will be greater than 25.05 seconds
e. What percent of the sample means will be greater than 25.05 but less than 27.05 seconds?"
This is the pvalue of Z when X = 27.05 subtracted by the pvalue of Z when X = 25.05.
X = 27.05
has a pvalue of 0.9916
X = 25.05
has a pvalue of 0.0154
0.9916 - 0.0154 = 0.9762
97.62% of the sample means will be greater than 25.05 but less than 27.05 seconds
Asked and answered elsewhere.
brainly.com/question/9247314
You obviously don't mind using "technology" (Brainly) to answer these questions. A graphing calculator can do quadratic regression on the sequence and tell you its formula.
If you want to do it by hand, you can write the equation
.. y = ax^2 +bx +c
and substitute three of the given points. Then solve the resulting three linear equations for a, b, and c.
.. 4 = a +b +c
.. 7 = 4a +2b +c
.. 12 = 9a +3b +c
Subtracting the first equation from the other two reduces this to
.. 3 = 3a +b
.. 8 = 8a +2b
The latter can be divided by 2, so reduces to
.. 4 = 4a +b
Subtracting the first of the reduced equations from this, you have
.. 1 = a
so
.. 3 = 3*1 +b
.. 0 = b
and
.. 4 = a + b + c = 1 + 0 + c
.. 3 = c
And your equation is
.. y = x^2 +3 . . . . . . as shown previously
brainly.com/question/9247314
You obviously don't mind using "technology" (Brainly) to answer these questions. A graphing calculator can do quadratic regression on the sequence and tell you its formula.
If you want to do it by hand, you can write the equation
.. y = ax^2 +bx +c
and substitute three of the given points. Then solve the resulting three linear equations for a, b, and c.
.. 4 = a +b +c
.. 7 = 4a +2b +c
.. 12 = 9a +3b +c
Subtracting the first equation from the other two reduces this to
.. 3 = 3a +b
.. 8 = 8a +2b
The latter can be divided by 2, so reduces to
.. 4 = 4a +b
Subtracting the first of the reduced equations from this, you have
.. 1 = a
so
.. 3 = 3*1 +b
.. 0 = b
and
.. 4 = a + b + c = 1 + 0 + c
.. 3 = c
And your equation is
.. y = x^2 +3 . . . . . . as shown previously
Answer:
the lower right matrix is the third correct choice
Step-by-step explanation:
Your problem statement shows that you have correctly selected the matrices representing the initial problem setup (middle left) and the problem solution (middle right).
Of the remaining matrices, the upper left is an incorrect setup, and the lower left is an incorrect solution matrix.
__
We notice that in the remaining matrices on the right that the (2,3) term is 0, and the (3,2) and (3,3) terms are both 1.
The easiest way to get a 0 in the 3rd column of row 2 is to add the first row to the second. When you do that, you get ...
Already, we see that the second row matches that in the lower right matrix.
The easiest way to get 1's in the last row is to divide that row by 0.15. When we do that, the (3,4) entry becomes 2100/0.15 = 14000, matching exactly the lower right matrix.
The correct choices here are the two you have selected, and <em>the lower right matrix</em>.
