The mean price of a gallon of milk at various stores is $2.60 with a standard deviation of $0.15. If the cost of milk at Target
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Answer:
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- <u>Part A: No, you cannot.</u>
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- <u>Part B: 0.4491</u>
Explanation:
<u>Part A:</u>
The mean of samples of symmetrical (bell shaped) distributions follow a normal distribution pattern.
Thus, for symmetrical distributions you can use the z-score tables to make calculations that permit calculate probabilities for particular values.
For <em>skewed </em>distributions, in general, the samples do not follow a normal distribution pattern, except that the samples are large.
Since <em>a sample of 20 pictures</em> is not large enough, the answer to this question is negative: <em>you cannot accurately calculate the probability that the mean picture size is more than 3.8MB for an SRS (skewed right sample) of 20 pictures.</em>
<u>Part B.</u>
For large samples, the<em> Central Limit Theorem</em> will let you work with samples from skewed distributions.
Although the distribution of a population is skewed, the <em>Central Limit Theorem</em> states that large samples follow a normal distribution shape.
It is accepted that samples of 30 data is large enough to use the <em>Central Limit Theorem.</em>
Hence, you can use the z-core tables for standard normal distributions to calculate the probabilities for a <em>random sample of 60 pictures</em> instead of 20.
The z-score is calculated with the formula:
- z-score = (value - mean/ (standard deviation).
Here, mean = 3.7MB, value = 3.8MB, and standard deviation = 0.78MB.
Thus:
Then, you must use the z-score table to find the probability that the z-score is greater than - 0.128.
There are tables that show the cumulative probability in the right end and tables that show the cumulative probability in the left end of a normal standard distribution .
The probability that a z-score is greater than -0.128 is taken directly from a table with the cumulative probability in the left end. It is 0.4491.
By definition, the perimeter of the triangle is the sum of its sides.
We must then use the formula of distance between points:
We now look for the longitus for each of the sides:
For L1:
For L2:
For L3:
Then, the perimeter is given by:
P = L1 + L2 + L3
Substituting values we have:
Answer:
the perimeter of triangle ABC is:
none of the above.
We must then use the formula of distance between points:
We now look for the longitus for each of the sides:
For L1:
For L2:
For L3:
Then, the perimeter is given by:
P = L1 + L2 + L3
Substituting values we have:
Answer:
the perimeter of triangle ABC is:
none of the above.