Mercury orbits the sun in 87 24/25 Earth days. Venus orbits the sun in 224 7/10 Earth days, and Mars orbits the sun in 686 49/50
1 answer:
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Answer:
a) Approximately normal.
b) The mean is 75 years and the standard deviation is 0.8485 years.
c) 0.9909 = 99.09% probability that the mean age exceeds 73 years
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 normal distributions can be solved using the z-score formula.
In a set with mean and standard deviation
, the z-score 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 p-value, 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
.
For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.
Sample of 50 retirees
This means that
Mean age and standard deviation are 75 and 6 years
This means that
a. Describe the shape of the sampling distribution of the sample mean in this case
By the Central Limit Theorem, approximately normal.
b. Find the mean and standard error of the sampling distribution of the sample mean.
By the Central Limit Theorem, the mean is 75 and the standard error is
c. What is the probability that the mean age exceeds 73 years?
This is 1 subtracted by the pvalue of Z when X = 73.
By the Central Limit Theorem
has a pvalue of 0.0091
1 - 0.0091 = 0.9909
0.9909 = 99.09% probability that the mean age exceeds 73 years
Answer:
The correct option is 1.
Step-by-step explanation:
The given parent function is
1. Domain of the function is all positive real number including 0.
2. Range of the function is all positive real number including 0.
3. It is an increasing function. It increases at decreasing rate.
First graph increase at decreasing rate and it starts from (-4,-1), therefore the required function is
Therefore graph 1 is an example of a function whose parent graph is of the form y = √x.
Second graph is a parabola, so it is the graph of a quadratic function.
Third graph is a rectangular hyperbola, so it is the graph of a rational functions.
Fourth graph is increasing at increasing rate, so it is the graph of an exponential function.
Therefore options 2, 3 and 4 are incorrect.
