A rectangular region is removed from another rectangular region to create the shaded region shown below. Find the area of the sh
aded region.
1 answer:
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Answer:
μ = 5.068 oz
Step-by-step explanation:
Normal distribution formula to use the table attached
Z = (x - μ)/σ
where μ is mean, σ is standard deviation, Z is on x-axis and x is a desired point.
98% of 6-oz. cups will not overflow means that the area below the curve is equal to 0.49; note that the curve is symmetrical respect zero, so, 98% of the cases relied between the interval (μ - some value) and (μ + some value)].
From table attached, area = 0.49 when Z = 2.33. From data, σ = 0.4 oz and x = 6 oz (maximum capacity of the cup). Isolating x from the formula gives
Z = (x - μ)/σ
2.33 = (6 - μ)/0.4
μ = 6 - 2.33*0.4
μ = 5.068
This means that with a mean of 5 oz and a standard deviation of 0.4 oz, the machine will discharge a maximum of 6 oz in the 98% of the cases.
In order to write 
as a percentage, we must first convert the fraction into a decimal. We can do that simply by dividing.
35 / 20 = 1.75
In order to convert a fraction to a decimal, we must multiply it by 100
1.75 * 100 = 175%
as a percentage is 175%.
Hope that helped =)
35 / 20 = 1.75
In order to convert a fraction to a decimal, we must multiply it by 100
1.75 * 100 = 175%
Hope that helped =)