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The number of accidents per week at a hazardous intersection is a random variable with mean 6.3 and standard deviation 5.85. The distributio
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The number of accidents per week at a hazardous intersection is a random variable with mean 6.3 and standard deviation 5.85. The distribution of the number of accidents is very right skewed. (a) Suppose we let X be the sample average number of accidents per week at the intersection during 9 randomly chosen weeks. What is the probability that X is less than 5
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2021-07-27T17:59:40+00:00
2021-07-27T17:59:40+00:00 1 Answers
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Answer:
The probability that X is less than 5 cannot be determined.
Step-by-step explanation:
Normal Probability Distribution:
Problems of normal distributions can be solved using the z-score formula.
In a set with mean
and standard deviation
, the z-score of a measure X is given by:
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 p-value, we get the probability that the value of the measure is greater than X.
Central Limit Theorem
The Central Limit Theorem estabilishes that, for a normally distributed random variable X, with mean
and standard deviation
, the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean
and standard deviation
.
For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.
In this question:
The distribution is right-skewed, which means that the central limit theorem can only be applied for a sample size of at least 30. Since the sample size is 9 < 30, the CLT cannot be applied, and thus the probability that X is less than 5 cannot be determined.