An electronic product takes an average of 4 hours to move through an assembly line. If the standard deviation is 0.5 hours, what is the probability that an item will take between 2.8 and 4.3 hours to move through the assembly line

0.7176

Step-by-step explanation:

We solve this question, using z score formula.

Z score formula = (x - μ)/σ

where x is the raw score

μ is the population mean

σ is the population standard deviation.

For z1, where x1 = 2.8, μ = 4, σ = 0.5

z score formula = (2.8 - 4)/0.5

= -2.4

We find the probability of the z score using the z score table.

P(x = 2.8) = P(z = -2.4)

= 0.0081975

For z2, where x2 = 4.3, μ = 4, σ = 0.5

z score formula = (4.3 - 4)/0.5

= 0.3/0.5

= 0.6

We find the probability of the z score using the z score table.

P(x = 4.3) = P(z = 0.6)

= 0.72575

The probability that an item will take between 2.8 and 4.3 hours to move through the assembly line is calculated as:

= 2.8 < x < 4.3

= P(z = 0.6) - P(z = -2.4)

= 0.72575 - 0.0081975

= 0.7175525

Approximately ≈ 0.7176

Therefore, the probability that an item will take between 2.8 and 4.3 hours to move through the assembly line is 0.7176

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step-by-step explanation: