Question

In: Statistics and Probability

Consider a binomial distribution of 200 trials with expected value 80 and standard deviation of about...

Consider a binomial distribution of 200 trials with expected value 80 and standard deviation of about 6.9. Use the criterion that it is unusual to have data values more than 2.5 standard deviations above the mean or 2.5 standard deviations below the mean to answer the following questions.

(a) Would it be unusual to have more than 120 successes out of 200 trials? Explain.

Yes. 120 is more than 2.5 standard deviations above the expected value.

Yes. 120 is more than 2.5 standard deviations below the expected value.

No. 120 is less than 2.5 standard deviations above the expected value.

No. 120 is less than 2.5 standard deviations below the expected value.

(b) Would it be unusual to have fewer than 40 successes out of 200 trials? Explain.

Yes. 40 is more than 2.5 standard deviations above the expected value.

Yes. 40 is more than 2.5 standard deviations below the expected value.

No. 40 is less than 2.5 standard deviations above the expected value.

No. 40 is less than 2.5 standard deviations below the expected value.

(c) Would it be unusual to have from 70 to 90 successes out of 200 trials? Explain.

No. 70 to 90 observations is within 2.5 standard deviations of the expected value.

Yes. 70 to 90 observations is within 2.5 standard deviations of the expected value.

No. 90 observations is more than 2.5 standard deviations above the expected value.

Yes. 70 observations is more than 2.5 standard deviations below the expected value.

Solutions

Expert Solution

1:- Standard Deviation is 6.9
2:- Standard Deviations are 13.8

Any number that is more than 13.8 away from the mean of 80 would be unusual.
80 - 13.8 = 66.2
80 + 13.8 = 93.8

Expected would be in the range 66.2 to 93.8.
Unusual would be a score below 66.2 or above 93.8.

(a) Would it be unusual to have more than 120 successes out of 200 trials? Explain.

120 is above 93.8 so that is definitely unusual.

Because

Yes. 120 is more than 2.5 standard deviations above the expected value.

(b) Would it be unusual to have fewer than 40 successes out of 200 trials? Explain.

40 is below 66.2 so that is definitely unusual .

Because   

Yes. 40 is more than 2.5 standard deviations below the expected value.

(c) Would it be unusual to have from 70 to 90 successes out of 200 trials? Explain.

70 and 90 are in the range and are not considered unusual.

Because 70 to 90 is within the range   

No. 70 to 90 observations is within 2.5 standard deviations of the expected value.

orchestra answered 2 years ago
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