Answer:
a. 95%
Step-by-step explanation:
We solve this question, using z score formula.
Z score formula = (x - μ)/σ/√n
where x is the raw score
μ is the population mean
σ is the population standard deviation.
n is number of samples
For z1, where x1 = 460, μ = 500, σ = 20, n = 140
z score formula = (460 - 500)/ 20
= -40/20
= -2
We find the probability of the z score using the z score table.
P(x = 460) = P(z = -2)
= 0.02275
For z2, where x2 = 540, μ = 500, σ = 20
z score formula = (540 - 500)/20
= 40/20
= 2
We find the probability of the z score using the z score table.
P(x = 540) = P(z = 2)
= 0.97725
The probability that the cargo containers will weigh between 460 pounds and 540 pounds is calculated as:
= 460 < x < 540
= P(z = 2) - P(z = -2)
= 0.97725 - 0.02275
= 0.9545
Converting to percentage
0.9545 × 100
= 95.45%
Therefore,the percentage of the cargo containers will weigh between 460 pounds and 540 pounds is 95%
