The number of vehicles leaving a turnpike at a certain exit during a particular
ID: 3158641 • Letter: T
Question
The number of vehicles leaving a turnpike at a certain exit during a particular time period has approximately a normal distribution with mean value 500 and standard deviation 75. Determine the probabilities below. (Round your answers to four decimal places.) (a) What is the approximate probability that the number of cars exiting during this period is at least 650?The number of vehicles leaving a turnpike at a certain exit during a particular time period has approximately a normal distribution with mean value 500 and standard deviation 75. Determine the probabilities below. (Round your answers to four decimal places.) (a) What is the approximate probability that the number of cars exiting during this period is at least 650?
(a) What is the approximate probability that the number of cars exiting during this period is at least 650?
Explanation / Answer
Let X be the random variable that The number of vehicles leaving a turnpike at a certain exit during a particular time period.
Given that X ~ Normal(mean=500, sd=75).
(a) What is the approximate probability that the number of cars exiting during this period is at least 650?
That is here we have to find P(X>=650).
Now first convert x = 650 into z-score.
z = (x - mean) / sd
z = (650 - 500) / 75 = 2
That is now we have to find P(Z>2).
P(Z>2) = 1 - P(Z<=2)
The folded probability wecan find by using EXCEL.
syntax is,
=NORMSDIST(z)
where z is test statistic value.
P(Z<=2) = 0.9772
P(Z>2) = 1 - 0.9772
P(Z>2) = 0.0228
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