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prohojiy [21]
3 years ago
12

Math sucks at times and we all know that. So, instead of coming onto Brainly for every answer to your math, this website gives y

ou the answers straight away, no typing the question or waiting hours for one. It doesn't have all the answers, just for specific textbooks, but these are the textbooks most people use so meh. Links below people https://www.slader.com/subject/math/homework-help-and-answers/
Mathematics
2 answers:
skelet666 [1.2K]3 years ago
8 0

Answer:

thanks

Step-by-step explanation:

BigorU [14]3 years ago
8 0

Answer:

ohhh ok thank you !!

Step-by-step explanation:

have an amazing rest of ur day and tyy! God Bless you :)))

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a) 0.6628 = 66.28% probability that at least 85 visitors had a recorded entry through the Beaver Meadows park entrance

b) 0.5141 = 51.41% probability that at least 80 but less than 90 visitors had a recorded entry through the Beaver Meadows park entrance

c) 0.5596 = 55.96% probability that fewer than 12 visitors had a recorded entry through the Grand Lake park entrance.

d) 0.9978 = 99.78% probability that more than 55 visitors have no recorded point of entry

Step-by-step explanation:

Binomial probability distribution

Probability of exactly x sucesses on n repeated trials, with p probability.

Can be approximated to a normal distribution, using the expected value and the standard deviation.

The expected value of the binomial distribution is:

E(X) = np

The standard deviation of the binomial distribution is:

\sqrt{V(X)} = \sqrt{np(1-p)}

Normal probability distribution

Problems of normally distributed samples can be solved using 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.

When we are approximating a binomial distribution to a normal one, we have that \mu = E(X), \sigma = \sqrt{V(X)}.

In this problem, we have that:

n = 175

(a) What is the probability that at least 85 visitors had a recorded entry through the Beaver Meadows park entrance?

46.7% of visitors to Rocky Mountain National Park in 2018 entered through the Beaver Meadows. This means that p = 0.467. So

\mu = E(X) = np = 175*0.467 = 81.725

\sigma = \sqrt{V(X)} = \sqrt{np(1-p)} = \sqrt{175*0.467*0.533} = 6.6

This probability, using continuity correction, is P(X \geq 85 - 0.5) = P(X \geq 84.5), which is 1 subtracted by the pvalue of Z when X = 84.5. So

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

Z = \frac{84.5 - 81.725}{6.6}

Z = 0.42

Z = 0.42 has a pvalue of 0.6628.

66.28% probability that at least 85 visitors had a recorded entry through the Beaver Meadows park entrance.

(b) What is the probability that at least 80 but less than 90 visitors had a recorded entry through the Beaver Meadows park entrance?

Using continuity correction, this is P(80 - 0.5 \leq X <  90 - 0.5) = P(79.5 \leq X \leq 89.5), which is the pvalue of Z when X = 89.5 subtracted by the pvalue of Z when X = 79.5. So

X = 89.5

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

Z = \frac{89.5 - 81.725}{6.6}

Z = 1.18

Z = 1.18 has a pvalue of 0.8810.

X = 79.5

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

Z = \frac{79.5 - 81.725}{6.6}

Z = -0.34

Z = -0.34 has a pvalue of 0.3669.

0.8810 - 0.3669 = 0.5141

51.41% probability that at least 80 but less than 90 visitors had a recorded entry through the Beaver Meadows park entrance

(c) What is the probability that fewer than 12 visitors had a recorded entry through the Grand Lake park entrance?

6.3% of visitors entered through the Grand Lake park entrance, which means that p = 0.063

\mu = E(X) = np = 175*0.063 = 11.025

\sigma = \sqrt{V(X)} = \sqrt{np(1-p)} = \sqrt{175*0.063*0.937} = 3.2141

This probability, using continuity correction, is P(X < 12 - 0.5) = P(X < 11.5), which is the pvalue of Z when X = 11.5. So

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

Z = \frac{11.5 - 11.025}{3.2141}

Z = 0.15

Z = 0.15 has a pvalue of 0.5596.

55.96% probability that fewer than 12 visitors had a recorded entry through the Grand Lake park entrance.

(d) What is the probability that more than 55 visitors have no recorded point of entry?

22.7% of visitors had no recorded point of entry to the park. This means that p = 0.227

\mu = E(X) = np = 175*0.227 = 39.725

\sigma = \sqrt{V(X)} = \sqrt{np(1-p)} = \sqrt{175*0.227*0.773} = 5.54

Using continuity correction, this probability is P(X \leq 55 + 0.5) = P(X \leq 55.5), which is the pvalue of Z when X = 55.5. So

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

Z = \frac{55.5 - 39.725}{5.54}

Z = 2.85

Z = 2.85 has a pvalue of 0.9978

0.9978 = 99.78% probability that more than 55 visitors have no recorded point of entry

8 0
3 years ago
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