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.

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

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