In a study of plant safety, it was found that the time it took for machine operators to react to a warning light was normally distributed with a mean 1 second and standard deviation 0.3 second. Suppose a warning light visible to 4 operators goes on. What is the probability that the average (mean) reaction time of the 4 operators exceeds 1.25 seconds?

Answers

Answer 1

Answer:

Answer:

4.75% probability that the average (mean) reaction time of the 4 operators exceeds 1.25 seconds.

Step-by-step explanation:

Central Limit Theorem

The Central Limit Theorem estabilishes that, for a random variable X, with mean $\mu$ and standard deviation $\sigma$ , a large sample size can be approximated to a normal distribution with mean $\mu$ and standard deviation $(\sigma)/(√(n))$

Normal probability distribution

Problems of normally distributed samples can be solved using the z-score formula.

In a set with mean $\mu$ and standard deviation $\sigma$ , the zscore of a measure X is given by:

$Z = (X - \mu)/(\sigma)$

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.

In this problem, we have that:

$\mu = 1, \sigma = 0.3, n = 4, s = (0.3)/(√(4)) = 0.15$

What is the probability that the average (mean) reaction time of the 4 operators exceeds 1.25 seconds?

This is 1 subtracted by the pvalue of Z when X = 1.25. So

$Z = (X - \mu)/(s)$

$Z = (1.25 - 1)/(0.15)$

$Z = 1.67$

$Z = 1.67$ has a pvalue of 0.9525.

So there is a 1-0.9525 = 0.0475 = 4.75% probability that the average (mean) reaction time of the 4 operators exceeds 1.25 seconds.

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Step-by-step explanation:

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Answers

Answer:

a) min: 0; max: 21

b) min: 34; max: 55

Step-by-step explanation:

In the attached Venn diagrams (part c), the overlap of the two circles represents the number on both teams.

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In the bottom diagram, there is complete overlap between the teams, so the maximum number that play both sports is 21 (the minimum team size of the two teams).

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Answers

Answer:

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Step-by-step explanation:

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Answers

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Answer:

Step-by-step explanation:

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