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Yakvenalex [24]
3 years ago
10

The average weight of the top 5 fish at a fishing tournament was 13.9 pounds. Some of the weights of the fish are shown in the t

able.
What was the weight of the heaviest fish?

Mathematics
1 answer:
Firdavs [7]3 years ago
3 0
The weight of the heaviest fish was either 13.2 or 14.8
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A sample size 25 is picked up at random from a population which is normally
Margarita [4]

Answer:

a) P(X < 99) = 0.2033.

b) P(98 < X < 100) = 0.4525

Step-by-step explanation:

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

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.

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.

Mean of 100 and variance of 36.

This means that \mu = 100, \sigma = \sqrt{36} = 6

Sample of 25:

This means that n = 25, s = \frac{6}{\sqrt{25}} = 1.2

(a) P(X<99)

This is the pvalue of Z when X = 99. So

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

By the Central Limit Theorem

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

Z = \frac{99 - 100}{1.2}

Z = -0.83

Z = -0.83 has a pvalue of 0.2033. So

P(X < 99) = 0.2033.

b) P(98 < X < 100)

This is the pvalue of Z when X = 100 subtracted by the pvalue of Z when X = 98. So

X = 100

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

Z = \frac{100 - 100}{1.2}

Z = 0

Z = 0 has a pvalue of 0.5

X = 98

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

Z = \frac{98 - 100}{1.2}

Z = -1.67

Z = -1.67 has a pvalue of 0.0475

0.5 - 0.0475 = 0.4525

So

P(98 < X < 100) = 0.4525

6 0
2 years ago
IM BEGGING YOU PLEASE HELP I WILL GIVE BRAINLIEST!!!!
tensa zangetsu [6.8K]

Answer: The second answer.

Step-by-step explanation:

3 0
2 years ago
HELP PLEASE<br><br><br> SHOW WORK<br> WILL MARK BRAINLIEST
defon

I've attached a photo of the solution below. Hope it helps!

3 0
2 years ago
I need help with this!!
dolphi86 [110]

Answer:

its 50

Step-by-step explanation:

6 0
2 years ago
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The expression below is scientific notation forwhat number? 4.29*10^-5
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.00429
I believe this is right! Have a good day!

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