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1. First of all arrange the data set in either ascending or descending order.
12, 19, 24, 26, 31, 38, 53. N = 7 (number of data items)
Median position = 1/2(N + 1)th item = 1/2(7 + 1)th item = 1/2(8)th item = 4th item = 26
First quatile = 1/4(N + 1)th item = 1/4(7 + 1)th item = 1/4(8)th item = 2nd item = 19
Third quatile = 3/4(N + 1)th item = 3/4(7 + 1)th item = 3/4(8)th item = 6th item = 38
Interquatile range = Third quartile - first quatile = 38 - 19 = 19
First, isolate 1/3s:
1/3s=12
Second, multiply both sides by 3 to get a singular value of s (just s):
s=36
A circle can be circumscribed about a quadrilateral if and only if the opposite angles of the quadrilater sum up to 180.
This is not the case, so you can't circumscribe a circle about the quadrilateral.
Answer: P(22 ≤ x ≤ 29) = 0.703
Step-by-step explanation:
Since the machine's output is normally distributed, we would apply the formula for normal distribution which is expressed as
z = (x - µ)/σ
Where
x = output of the machine in ounces per cup.
µ = mean output
σ = standard deviation
From the information given,
µ = 27
σ = 3
The probability of filling a cup between 22 and 29 ounces is expressed as
P(22 ≤ x ≤ 29)
For x = 22,
z = (22 - 27)/3 = - 1.67
Looking at the normal distribution table, the probability corresponding to the z score is 0.047
For x = 29,
z = (29 - 27)/3 = 0.67
Looking at the normal distribution table, the probability corresponding to the z score is 0.75
Therefore,
P(22 ≤ x ≤ 29) = 0.75 - 0.047 = 0.703
