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Gemiola [76]
2 years ago
15

Please answer this question

Mathematics
1 answer:
Yuki888 [10]2 years ago
4 0

Answer:

17.3

Step-by-step explanation:

a² = b² + c² - 2bc cos A

t² = 11² + 14² - 2(11)(14) cos 87

t² = 121 + 196 - 308 (.052336)

t² = 300.88

t = 17.3

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Assume that the empirical rule is a good model for the time it takes for all passengers to board an airplane. The mean time is 4
slamgirl [31]

Answer:

The interval that describes how long it takes for passengers to board the middle 95% of the time is between 40.16 minutes and 55.84 minutes.

Step-by-step explanation:

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.

In this problem, we have that:

\mu = 48, \sigma = 4.

Which interval describes how long it takes for passengers to board the middle 95% of the time?

This is between the 2.5th percentile and the 97.5th percentile.

So this interval is the value of X when Z has a a pvalue of 0.025 and the value of X when Z has a pvalue of 0.975

Lower Limit

Z has a pvalue of 0.025 when Z = -1.96. So

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

-1.96 = \frac{X - 48}{4}

X - 48 = -1.96*4

X = 40.16

Upper Limit

Z has a pvalue of 0.975 when Z = 1.96. So

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

1.96 = \frac{X - 48}{4}

X - 48 = 1.96*4

X = 55.84

The interval that describes how long it takes for passengers to board the middle 95% of the time is between 40.16 minutes and 55.84 minutes.

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2- went up 7%


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