Mathematics, 30.03.2020 23:44 ahmetagayew2004

The length of time it takes college students to find a parking spot in the library parking lot follows a normal distribution with a mean of 3.5 minutes and a standard deviation of 1 minute. Find the probability that a randomly selected college student will take between 2.0 and 4.5 minutes to find a parking spot in the library lot. Report the probability to 3 decimal places.

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0.774 = 77.40% probability that a randomly selected college student will take between 2.0 and 4.5 minutes to find a parking spot in the library lot.

Step-by-step explanation:

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:

$Z = \frac{X - \mu}{\sigma}$

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:

$\mu = 3.5, \sigma = 1$

Find the probability that a randomly selected college student will take between 2.0 and 4.5 minutes to find a parking spot in the library lot.

pvalue of Z when X = 4.5 subtracted by the pvalue of Z when X = 2. So

X = 4.5

$Z = \frac{X - \mu}{\sigma}$

$Z = \frac{4.5 - 3.5}{1}$

Z = 1

Z = 1 has a pvalue of 0.841

X = 2

$Z = \frac{X - \mu}{\sigma}$

$Z = \frac{2 - 3.5}{1}$

Z = -1.5

Z = -1.5 has a pvalue of 0.067

0.841 - 0.067 = 0.774

0.774 = 77.40% probability that a randomly selected college student will take between 2.0 and 4.5 minutes to find a parking spot in the library lot.

Answer from: Quest

you answer is a

step-by-step explanation:

Answer from: Quest

to plot points for x just start at the origin (middle) and go to the left however many times it say(if the number is a positive) if the number is a negative then go right however many times it says if it is 0 go nowhere

now keep you pencil there and go up however many times it says on y(if it is positive) if it is negative then go down however many times it says. if it says 0 go nowhere.

you have just plotted a point! now when you finish plotting all of them connect them with a ruler

plot each point as (-3, 7), (0,4), (3,1), (8,-4) in the parenthesis on the left of the comma is x and the right is y.

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