Mathematics, 28.06.2021 15:10, dorothybean

Police response time to an emergency call is the difference between the time the call is first received by the dispatcher and the time a patrol car radios that it has arrived at the scene. Over a long period of time, it has been determined that the police response time has a normal distribution with a mean of 8.1 minutes and a standard deviation of 2.0 minutes. For a randomly received emergency call, find the following probabilities. a. between 5 and 10 min
b. less than 5 min
c. more than 10 min

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answered: jbug6780

a) 0.7683 = 76.83% probability that a randomly selected emergency call is between 5 and 10 minutes.

b) 0.0606 = 6.06% probability that a randomly received emergency call is of less than 5 min.

c) 0.1711 = 17.11% probability that a randomly received emergency call is of more than 10 min.

Step-by-step explanation:

Normal Probability Distribution:

Problems of normal distributions can be solved using the z-score formula.

In a set with mean $\mu$ and standard deviation $\sigma$ , the z-score 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 p-value, we get the probability that the value of the measure is greater than X.

Mean of 8.1 minutes and a standard deviation of 2.0 minutes.

This means that $\mu = 8.1, \sigma = 2$

a. between 5 and 10 min

This is the p-value of Z when X = 10 subtracted by the p-value of Z when X = 5.

X = 10

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

$Z = \frac{10 - 8.1}{2}$

Z = 0.95

Z = 0.95 has a p-value of 0.8289

X = 5

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

$Z = \frac{5 - 8.1}{2}$

Z = -1.55

Z = -1.55 has a p-value of 0.0606

0.8289 - 0.0606 = 0.7683

0.7683 = 76.83% probability that a randomly selected emergency call is between 5 and 10 minutes.

b. less than 5 min

p-value of Z when X = 5, which, found from item a, is of 0.0606

0.0606 = 6.06% probability that a randomly received emergency call is of less than 5 min.

c. more than 10 min

1 subtracted by the p-value of Z when X = 10, which, from item a, is of 0.8289

1 - 0.8289 = 0.1711

0.1711 = 17.11% probability that a randomly received emergency call is of more than 10 min.

answered: Guest

a. 32 degrees

step-by-step explanation:

here we have to use the rule.

m∠e = 1/2 (major arc - minor arc)

m∠e = 1/2 (212 - 148)

m∠e = 1/2 (64)

m∠e = 32 degrees

answer: a. 32 degrees

you

In the diagram below, and are tangent to o. what is the measure of e?

answered: Guest

answer: 1475

step-by-step explanation:

becuase you have to know what they are asking you

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