A company produces steel rods. The lengths of the steel rods are normally distributed with a mean of 164.6-cm and a standard deviation of 2.4-cm. For shipment, 27 steel rods are bundled together. Find the probability that the average length of a randomly selected bundle of steel rods is less than 164.2-cm. P(M < 164.2-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. Question Holp:
Continuous Probability Distributions
Probability distributions are of two types, which are continuous probability distributions and discrete probability distributions. A continuous probability distribution contains an infinite number of values. For example, if time is infinite: you could count from 0 to a trillion seconds, billion seconds, so on indefinitely. A discrete probability distribution consists of only a countable set of possible values.
Normal Distribution
Suppose we had to design a bathroom weighing scale, how would we decide what should be the range of the weighing machine? Would we take the highest recorded human weight in history and use that as the upper limit for our weighing scale? This may not be a great idea as the sensitivity of the scale would get reduced if the range is too large. At the same time, if we keep the upper limit too low, it may not be usable for a large percentage of the population!
Obtain the standard z-score for the random variable M equals 164.2 cm.
The standard z-score for the random variable M equals 164.2 cm is obtained below as follows:
The standard z-score for the random variable M equals 164.2 cm is –0.167.
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