A company produces steel rods. The lengths of the steel rods are normally distributed with a mean of 125.2-cm and a standard deviation of 2.3-cm. For shipment, 25 steel rods are bundled together.Find the probability that the average length of a randomly selected bundle of steel rods is less than 124.5-cm.P(M < 124.5-cm) =Enter your answer as a number accurate to 4 decimal places. Answers obtained using exact z-scores or z-scores rounded to 3 decimal places are accepted.

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contexto1024 contexto1024 · Answer 1 · 2022-12-03T04:49:54+01:00

The probability that the average length of a randomly selected bundle of steel rods is less than 124.5-cm i.e.,

P(M < 124.5-cm) is 0.0603..

We have Given that,

The lengths of the steel rods are Normally distributed.

mean of distribution (μ) = 125.2

standard deviation (σ) = 2.3

Sample size (n) = 25

Standard error = σ/√n = 2.3 /√25 = 0.46

convert to P(z < ???) using transformation to z-statistic which is N(0,1):

P(z < (M - population mean)/(standard deviation/square root(sample size))

P(M < 124.5 ) = P[(M - μ ) /σ /√n < ( 124.5 - 125.2 ) /0.46 ]

= P( z < -1.522 )

Using z table,

= 0.0603

Probability = 0.0603

Hence, the Z-score is -1.52 and the required probability is 0.0603

For more information about Probability of normal distribution, refer:

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