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SKYBLUE1015
05.09.2020 •
Mathematics
Assume that round widgets from a manufacturing process have diameters that are normally distributed with mean 135.75 centimeters and standard deviation 1.85 centimeters. The chances that a randomly selected widget has diameter between 129 centimeters and 143 centimeters is closest to which of the following?a. 99,999 out of 100,000.
b. 99 out of 100.
c. 999 out of 1,000.
d. 9,999 out of 10,000.
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Ответ:
b. 99 out of 100.
Step-by-step explanation:
We solve for this using z score formula
z-score formula is given as:
z = (x - μ)/σ
where
x is the raw score
μ is the population mean
σ is the population standard deviation.
a) x = 129cm, μ = 135.75cm, σ = 1.85cm
z = (129- 135.75)/1.85
z = -3.64865
Finding the Probability value of the z score from the z table:
P(x = 129) = P(z = -3.64865)
= 0.00013181
b) x = 143 cm, μ = 135.75cm, σ = 1.85cm
z = (143- 135.75)/1.85
z = 3.91892
Finding the Probability value of the z score from the z table:
P(x = 143) = P(z = 3.91892)
= 0.99996
The chances that a randomly selected widget has diameter between 129 centimeters and 143centimeters
= P(x = 143) - P(x = 129)
= P(z = 3.91892) - P(z = -3.64865)
= 0.99996 - 0.00013181
= 0.99982819
Converting to percentage
= 0.99982819 × 100
= 99.982819%
Therefore, option b. 99 out of 100 is the correct answer
Ответ:
Step-by-step explanation:
dude its not that hard