The mean cost of renting an apartment in a city is $2000 per month with a standard deviation of $300. Let ?̅ denote the mean cost of rent for a random sample of 60 apartments in this city. 5. The mean ?D̅ and the standard deviation ?D̅ of ?̅ are: (a) ?D̅ = 33.33 ?D̅ = 38.73, (b) ?D̅ = 33.33 ?D̅ = 5, (c) ?D̅ = 2000 ?D̅ = 38.73, (d) ?D̅ = 2000 ?D̅ = 5, (e) ?D̅ = 2000 ?D̅ = 300,
Inverse Normal Distribution
The method used for finding the corresponding z-critical value in a normal distribution using the known probability is said to be an inverse normal distribution. The inverse normal distribution is a continuous probability distribution with a family of two parameters.
Mean, Median, Mode
It is a descriptive summary of a data set. It can be defined by using some of the measures. The central tendencies do not provide information regarding individual data from the dataset. However, they give a summary of the data set. The central tendency or measure of central tendency is a central or typical value for a probability distribution.
Z-Scores
A z-score is a unit of measurement used in statistics to describe the position of a raw score in terms of its distance from the mean, measured with reference to standard deviation from the mean. Z-scores are useful in statistics because they allow comparison between two scores that belong to different normal distributions.
The
5. The mean ?D̅ and the standard deviation ?D̅ of ?̅ are:
(a) ?D̅ = 33.33 ?D̅ = 38.73, (b) ?D̅ = 33.33 ?D̅ = 5, (c) ?D̅ = 2000 ?D̅ = 38.73, (d) ?D̅ = 2000 ?D̅ = 5, (e) ?D̅ = 2000 ?D̅ = 300,
Denote X as the mean cost of renting an apartment in a city. It is given that X is distributed, with mean μ = $2000 and standard deviation σ = $300.
A random sample of 60 apartments are taken.
As the sample size is large (>30), it can be assumed that the mean cost of renting an apartment in a city follows normal distribution with mean μ = $2000 and standard deviation σ = $300.
For this problem let us assume ?¯ is same as X bar.
Let X bar be the mean cost rent for the sample. It is known that,
Therefore, in this situation,
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