Answer:
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
