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Answer:
The mean of the sampling distribution of means for SRS of size 50 is and the standard deviation is
By the Central Limit Theorem, since we have of sample of 50, which is larger than 30, it does not matter that the underlying population distribution is not normal.
0% probability a sample of 50 people will wait longer than 45 seconds for an elevator.
Step-by-step explanation:
To solve this problem, 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 random variable X, with mean and standard deviation
, a large sample size, of at least 30, can be approximated to a normal distribution with mean
and standard deviation
In this problem, we have that:
What are the mean and standard deviation of the sampling distribution of means for SRS of size 50?
By the Central Limit Theorem
The mean of the sampling distribution of means for SRS of size 50 is and the standard deviation is
Does it matter that the underlying population distribution is not normal?
By the Central Limit Theorem, since we have of sample of 50, which is larger than 30, it does not matter that the underlying population distribution is not normal.
What is the probability a sample of 50 people will wait longer than 45 seconds for an elevator?
We have to use 45 seconds as minutes, since the mean and the standard deviation are in minutes.
Each minute has 60 seconds.
So 45 seconds is 45/60 = 0.75 min.
This probability is 1 subtracted by the pvalue of Z when X = 0.75. So
By the Central Limit Theorem
has a pvalue of 1
1-1 = 0
0% probability a sample of 50 people will wait longer than 45 seconds for an elevator.
- Quadratic Formula:
, with a = x^2 coefficient, b = x coefficient, and c = constant.
Firstly, starting with the y-intercept. To find the y-intercept, set the x variable to zero and solve as such:
<u>Your y-intercept is (0,-51).</u>
Next, using our equation plug the appropriate values into the quadratic formula:
Next, solve the multiplications and exponent:
Next, solve the addition:
Now, simplify the radical using the product rule of radicals as such:
- Product Rule of Radicals: √ab = √a × √b
√1224 = √12 × √102 = √2 × √6 × √6 × √17 = 6 × √2 × √17 = 6√34
Next, divide:
<u>The exact values of your x-intercepts are (-4 + √34, 0) and (-4 - √34, 0).</u>
Now to find the approximate values, solve this twice: once with the + symbol and once with the - symbol:
<u>The approximate values of your x-intercepts (rounded to the hundredths) are (1.83,0) and (-9.83,0).</u>
Answer:
C. V = two-thirds (27)
Step-by-step explanation:
Given
Solid Shapes: Cylinder and Sphere
Volume of Cylinder = 27π ft³
Required
Volume of the sphere.
From the question,
<u>We have that</u>
1. The volume of the sphere is the same as the volume of the cylinder
2. The height of the sphere is the same as the height of the cylinder.
From (2) above;
This means that the height of the cylinder equals the diameter of the sphere.
Let h represent the height of the sphere and d represent the diameter of sphere.
Mathematical, d = h
Recall that radius, r =
Substitute h for d in the above expression
. ----- (take note of this)
Calculating the volume of a cylinder.
V = πr²h
Recall that V = 27; This gives us
27 = πr²h
Divide both sides by h
-------------------
Calculating the volume of a sphere
Expand the above expression
Substitute
Recall that
So,
V = two-third (27)