If a uniform distribution is defined over the interval from 6 to 10, then answer the followings: I. What is the mean of this uniform distribution? II. Show that the probability of any value between 6 and 10 is equal to 1.0 III. Find the probability of a value more than 7. IV. Find the probability of a value between 7 and 9. The closing price of Schnur Sporting Goods Inc. common stock is uniformly distributed between $20 and $30 per share. What is the probability that the stock price will be: V. More than $27? VI. Less than or equal to $24? The April rainfall in Flagstaff, Arizona, follows a uniform distribution between 0.5 and 3.00 inches. VII. What is the mean amount of rainfall for the month? VIII. What is the probability of less than an inch of rain for the month? IX. What is the probability of exactly 1.00 inch of rain? X. What is the probability of more than 1.50 inches of rain for the month?
Transcribed Image Text:Mean
Std. dev. X
Result reater/Less/Betwee Answer
Q 11
50
4
44
50
4
55
Between 44-55
Q12
50
4
55
Greater than 55
Q13
50
4
52
50
4
55
Between 52-55
Q14
3401
82.5
3500
More than 3500
Q15
3401
82.5
3500
3401
82.5
3579
Between 3500-3579
Q16
3401
82.5
3325
3401
82.5
3579
Between 3325-3579
Q17
15
3.5
20
More than 20
Q18
15
3.5
20
Less than 20
Q19
15
3.5
10
15
3.5
12
Between 10-12
Q20
15
3.5
15
15
3.5
20
Between 15-20
Definition Definition Measure of central tendency that is the average of a given data set. The mean value is evaluated as the quotient of the sum of all observations by the sample size. The mean, in contrast to a median, is affected by extreme values. Very large or very small values can distract the mean from the center of the data. Arithmetic mean: The most common type of mean is the arithmetic mean. It is evaluated using the formula: μ = 1 N ∑ i = 1 N x i Other types of means are the geometric mean, logarithmic mean, and harmonic mean. Geometric mean: The nth root of the product of n observations from a data set is defined as the geometric mean of the set: G = x 1 x 2 ... x n n Logarithmic mean: The difference of the natural logarithms of the two numbers, divided by the difference between the numbers is the logarithmic mean of the two numbers. The logarithmic mean is used particularly in heat transfer and mass transfer. ln x 2 − ln x 1 x 2 − x 1 Harmonic mean: The inverse of the arithmetic mean of the inverses of all the numbers in a data set is the harmonic mean of the data. 1 1 x 1 + 1 x 2 + ...
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