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Harlamova29_29 [7]
3 years ago
15

A town has two fire engines operating independently. The probability that a specific engine is available when needed is 0.96. (a)

What is the probability that neither is available when needed? (b) What is the probability that a fire engine is available when needed?
Mathematics
1 answer:
o-na [289]3 years ago
8 0

Answer:

Answer is

a. P (both pumps not available) = 0.016

b. P (both pumps available) = 0.984

Step-by-step explanation:

a. Probability of neither pump is available.

We know that P1 + P2 = 1

P1 = Probability of one pump is available = 0.96

P2 = Probability of a pump not available = 1-0.96 = 0.04

Now the probability of both pump not available will be = P2 x P2

=0.04 x 0.04 = 0.016

b. Probability of both pumps available will be.

Using the equation of probability

P (both pumps available) + P (both pumps unavailable) = 1

P (both pumps available) = (1- P (both pumps unavailable))

P (both pumps available) = 1-0.016

P (both pumps available) = 0.984

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x = 56/8 = 7

x = 7
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Each friend got 6 cars each

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17-5= 12 cars

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Since there are 2 friends, you divide the cars given away by 2, hence

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What is the rule for the pattern 3 12 6 24 12 48 24
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4 years ago
The amount people pay for cable service varies quite a bit but the mean monthly fee is $142 and the standard deviation is $29. t
zhuklara [117]

Answer:

a) By the Central Limit Theorem, the mean is $142 and the standard deviation is $0.7488.

b) By the Central Limit Theorem, approximately normal.

c) 0.0901 = 9.01% probability that the average cable service paid by the sample of cable service customers will exceed $143

Step-by-step explanation:

To solve this question, we need to understand the normal probability distribution and the central limit theorem.

Normal probability distribution

When the distribution is normal, we use 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.

Central Limit Theorem

The Central Limit Theorem estabilishes that, for a normally distributed random variable X, with mean \mu and standard deviation \sigma, the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean \mu and standard deviation s = \frac{\sigma}{\sqrt{n}}.

For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.

The mean monthly fee is $142 and the standard deviation is $29.

This means that \mu = 142, \sigma = 29

Part a: what are the mean an standard deviation of the sample distribution of x hat show your work and justify your reasoning.

Sample of 1500(larger than 30).

By the Central Limit Theorem

The mean is $142

The standard deviation is s = \frac{29}{\sqrt{1500}} = 0.7488

Part b: what is the shape of the sampling distribution of x hat justify your answer.

By the Central Limit Theorem, approximately normal.

Part C: what is the probability that the average cable service paid by the sample of cable service customers will exceed $143?

This is 1 subtracted by the pvalue of Z when X = 143. So

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

By the Central Limit Theorem

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

Z = \frac{143 - 142}{0.7488}

Z = 1.34

Z = 1.34 has a pvalue of 0.9099

1 - 0.9099 = 0.0901

0.0901 = 9.01% probability that the average cable service paid by the sample of cable service customers will exceed $143

4 0
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