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forsale [732]
2 years ago
9

The distribution of passenger vehicle speeds traveling on a certain freeway in California is nearly normal with a mean of 73.7 m

iles/hour and a standard deviation of 4.72 miles/hour. The speed limit on this stretch of the freeway is 70 miles/hour.
(a) A highway patrol officer is hidden on the side of the freeway. What is the probability that 5 cars pass and none are speeding?
Assume that the speeds of the cars are independent of each other. (Round your answer to four decimal places.)
(b) On average, how many cars would the highway patrol officer expect to watch until the first car that is speeding?
(c) What is the standard deviation of the number of cars he would expect to watch?
Mathematics
1 answer:
umka2103 [35]2 years ago
5 0

Answer:

a)  0.2347, 0.0007

b) 1.30

c) 0.63

Step-by-step explanation:

Given –  

Mean = 73.4

Sigma = 4.7

Probability that the speed is greater than 70 is  

P (X>70) = P (z> (70-73.4)/4.7) = P (z>-0.72) = 0.7653

a) The probability that a car is not speeding = 1 - 0.7653 = 0.2347

The probability that all 5 cars are not speeding = (0.2347)5 = 0.0007

b) E (X) = 1/p = 1/0.7653 = 1.30  

c) Standard deviation = Sqrt (1-p/p) = (1-0.7653)/0.7653 = 0.63

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A CBS News/New York Times opinion poll asked 1,190 adults whether they would prefer balancing the federal budget over cutting ta
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Using the <u>normal distribution and the central limit theorem</u>, it is found that there is a 0.0166 = 1.66% probability of a sample proportion of 0.59 or less.

In a normal distribution with mean \mu and standard deviation \sigma, the z-score of a measure X is given by:

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

  • It 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, which is the percentile of X.
  • By the Central Limit Theorem, the sampling distribution of sampling proportions of a proportion p in a sample of size n has mean \mu = p and standard error s = \sqrt{\frac{p(1 - p)}{n}}

In this problem:

  • 1,190 adults were asked, hence n = 1190
  • In fact 62% of all adults favor balancing the budget over cutting taxes, hence p = 0.62.

The mean and the standard error are given by:

\mu = p = 0.62

s = \sqrt{\frac{p(1 - p)}{n}} = \sqrt{\frac{0.62(0.38)}{1190}} = 0.0141

The probability of a sample proportion of 0.59 or less is the <u>p-value of Z when X = 0.59</u>, hence:

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

By the Central Limit Theorem

Z = \frac{X - \mu}{s}

Z = \frac{0.59 - 0.62}{0.0141}

Z = -2.13

Z = -2.13 has a p-value of 0.0166.

0.0166 = 1.66% probability of a sample proportion of 0.59 or less.

You can learn more about the <u>normal distribution and the central limit theorem</u> at brainly.com/question/24663213

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How many ways can 6 people be chosen and arranged in straight line if there are 8 people to choose from? a. 48.b. 720.c. 20, 160
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<h2>C. <em>20,160</em></h2>

Step-by-step explanation:

This question bothers on permutation since we are to select a some people out of a group of people and then arrange in a straight line. If r object are to be arranged in a straight line when selecting them from n pool of objects. This can be done in nPr number of ways.

nPr = n!/(n-r)!

Selection of 6 people out of 8 people can therefore be done in 8C6 number of ways.

8P6 = 8!/(8-6)!

8P6 = 8!/2!

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Deposit $500 4% interest 2 years
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500 x 0.04 x 2 = 40

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