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Kaylis [27]
2 years ago
14

True or False: The amount of time it takes to complete an examination has a left skewed distribution with a mean of 65 minutes a

nd a standard deviation of 8 minutes. If 64 students were randomly sampled, the probability that the sample mean of the sampled students exceeds 71 minutes is approximately 0.
Mathematics
1 answer:
nekit [7.7K]2 years ago
6 0

Answer:

True

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 normally distributed samples are 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.

Central limit theorem:

The Central Limit Theorem estabilishes that, for a random variable X, with mean \mu and standard deviation \sigma, the sample means with size n of at least 30 can be approximated to a normal distribution with mean \mu and standard deviation s = \frac{\sigma}{\sqrt{n}}

In this problem, we have that:

\mu = 65, \sigma = 8, n = 64, s = \frac{8}{\sqrt{64}} = 1

If 64 students were randomly sampled, the probability that the sample mean of the sampled students exceeds 71 minutes is approximately 0.

This probability is 1 subtracted by the pvalue of Z when X = 71. So

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

By the Central Limit Theorem

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

Z = \frac{71 - 65}{1}

Z = 6

Z = 6 has a pvalue very close to 1.

1 - 1 = 0.

So approximately 0 probability that the sample mean of the sampled students exceeds 71 minutes.

The answer is true.

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Step-by-step explanation:

there is something wrong with your question.

there is no parallelogram with 8 and 6 ft side lengths that has an area of 54 ft².

the maximum area of a parallelogram with 8 and 6 ft side lengths is 48 ft². and that is a rectangle 8×6 as a special form of a parallelogram.

the area of any parallelogram is calculated

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and height is the length of the line perpendicular to the base line to one of the corners on the opposite side (as long as the base line).

if Ap = 54, and the base length is 8, this means

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height = 54/8 = 6.75 ft

but the height can only be the length of a side connected to the base line or less. not longer.

and in our example here, this connected side is 6. so, the height can only be 6 or less. not 6.75.

so, there must be something wrong with your numbers.

once you get the actual numbers, use my approach above with them (replace whatever number is wrong here by the true value).

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bagirrra123 [75]
FOR THE FIRST PROBLEM:

Differentiating p^2 + 2q^2 = 1100 with respect to time => 2p(dp/dt) + 4q(dq/dt) = 0 

<span>dp/dt = -2q/p(dq/dt) </span>

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I hope my answer has come to your help. Thank you for posting your question here in Brainly. We hope to answer more of your questions and inquiries soon. Have a nice day ahead!
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