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.

(a) yes. 120 is more than 2.5 standard deviations above the expected value.
(b) yes. 120 is more than 2.5 standard deviations below the expected value.
(c) no. 120 is less than 2.5 standard deviations above the expected value.
(d) no. 120 is less than 2.5 standard deviations below the expected value.

The correct answer is option 'a' : 120 is more than 2.5 standard deviations above the expected value.

Step-by-step explanation:

For an exponential distribution we have

The expected value μ = 80

No of trails n = 200

Thus we have

The deviation is related to expected value and probability as

Thus the values between the given deviation is

Now since 120 successes are out of the range of [62.75,97.25] thus 120 is more than the expected value.

b. 1.25 hr

step-by-step explanation:

if you have a constant speed of 60 mph, then you have a ratio between 60 mi. to 1 hr. dividing both sides by 60 we get the ratio

1 mi. to

then mult. both sides by 75 we get the ratio

75 mi. to

simplifying we get

75 mi. to

or 1.25 hr.

∈3,600

step-by-step explanation: