Mathematics: The previous exercises states that the distribution of speeds of cars traveling on the Interstate 5 Freeway (I-5) in California is nearly normal with a mean of 72.6 miles/hour and a standard deviation of 4.78 miles/hour. The speed limit on this stretch of the I-5 is 70 miles/hour. 5. 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.

The previous exercises states that the distribution

Ответ:

alazayjaime1423

03.02.2022

Mathematics

The probability is $P(X \le 70 ) = 0.7054$

Step-by-step explanation:

From the question we are told that

The mean is $\mu = 72.6 \ miles /hour$

The standard deviation is $\sigma = 4.78 \ miles /hour$

The speed limit is $x = 70 \ miles /hour$

Generally the probability that 5 cars pass and none are speeding is equivalent to the probability that the speed of the cars is less than x which is mathematically represented as

$P(X \le x ) = 1 - P(X x )$

Now

$P(X x) = P(\frac{X - \mu}{\sigma } \frac{x - \mu}{\sigma } )$

Generally

$\frac{X - \mu}{\sigma } = Z (The \ standardized \ value \ of \ X)$

$P(X 70) = P(Z \frac{70 - 72.6}{72.6 } )$

P(X 70) = P(Z -0.54 )

From the z-table

P(Z -0.54 ) = 0.2946

=> P(X 70) = 0.2946

$P(X \le 70 ) = 1 - P(X 70 )$

=> $P(X \le 70 ) = 1 - 0.2946$

=> $P(X \le 70 ) = 0.7054$

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Ответ:

dessyrob05

30.11.2021

Mathematics

a, b, d, f

Step-by-step explanation:

1. E

2. D

3. G

4. E

5. N

6. U

7. I

8. T

9. Y

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