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2 years ago

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The Amboy Kennel Club has held an annual dog show for the last 42 years. During this time he winner of "Best of Show" has been a

n Alaskan Malamute 21 times, a Great Pyrenees 3 times, and an Siberian Husky 18 times. Determine the empirical probability that the next winner of "Best of Show" will be a Great Pyrenees.

1 answer:

dmitriy555 [2]2 years ago

5 0

Answer:

0.071

Step-by-step explanation:

Number of wins by Alaskan Malamute = 21

Number of win by Great Pyrenees = 3

Number of wins by Siberian Husky = 18

Total number of shows = 42

We need to calculate the empirical probability that next winner will be a Great Pyrenees.

Empirical probability is defined as the ratio of the number of times a specific event occurs to total number of possibilities of all events being considered. In given case, the event that best of the show was a Great Pyrenees occurred 3 times, and total number of events were 42. So,

Empirical Probability that next winner will be a Great Pyrenees = $\frac{3}{42}=0.071$

Hence, the empirical probability that the next winner of "Best of Show" will be a Great Pyrenees is 0.071

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A jar of 150 jelly beans contains 22 red jelly beans, 38 yellow, 20 green, 28 purple, 26 blue, and the rest are orange.Let B = t

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Answer:

$P(R\ and\ B) = 0.0256$

Step-by-step explanation:

Given

$Red = 22$

$Yellow = 38$

$Green = 20$

$Purple = 28$

$Blue = 26$

$Orange = 16$

Required

Determine the probability of red then blue jelly? i.e. P(R and B)

From the question, we understand that the red jelly bean was not replaced. This means that the number of jelly beans reduced by 1 after the picking of the red jelly bean

So, we have:

$P(R\ and\ B) = P(R)\ and\ P(B)$

This is then solved further as:

$P(R\ and\ B) = P(R)\ *\ P(B)$

$P(R\ and\ B) = \frac{n(R)}{Total}\ *\frac{n(B)}{Total - 1}$

The probability has a denominator of Total - 1 because the number of jelly beans reduced by 1 after the picking of the red jelly bean

The equation becomes:

$P(R\ and\ B) = \frac{22}{150}\ *\frac{26}{150- 1}$

$P(R\ and\ B) = \frac{22}{150}\ *\frac{26}{149}$

$P(R\ and\ B) = \frac{22*26}{150*149}$

$P(R\ and\ B) = \frac{572}{22350}$

$P(R\ and\ B) = 0.02559284116$

$P(R\ and\ B) = 0.0256$

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Step-by-step explanation:

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Answer:

Step-by-step explanation:

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Answer:

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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:

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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 $s = \frac{\sigma}{\sqrt{n}}$ .

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Distribution of years of experience:

Mean 3, so $\mu = 3$

Standard deviation 2, so $\sigma = 2$

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1 subtracted by the pvalue of Z when X = 3.5. So

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

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$Z = 0.5$ has a pvalue of 0.6915

1 - 0.6915 = 0.3085

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