The number of passengers who arrive at the platform of a subway station for the 10 am train is a random variable with a mean of 120 and a variance of 16. Find the lower bound of the probability that there will be between 100 and 140 passengers (round off to second decimal place).

The lower bound of the probability that there will be between 100 and 140 passengers 96%.

Step-by-step explanation:

The Chebyshev's theorem states that, the probability that X is within k standard deviation of mean is given by,

Here, k is any positive number.

The given information is:

Mean (µ) = 120

Standard deviation (σ) = 16.

Then, we need to compute, P (100 ≤ X ≤ 140).

Then,  

Since, these two values coincide it implies that the event (66000, 78000) is centered about the mean.

Also, the event P (100 ≤ X ≤ 140) is equivalent to having X within 5 standard deviation of the mean.  

That is, k = 5.

Then for k = 5,  

That is, P (100 ≤ X ≤ 140) ≤ 0.96 .

Thus, the lower bound of the probability that there will be between 100 and 140 passengers 96%.

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step-by-step explanation:

if you want to solve percent error follow these steps.

1. subtract the accepted value from the experimental value.

2. take the absolute value of step 1.

3. divide that answer by the accepted value.

4. multiply that answer by 100 and add the % symbol to express the answer as a percentage.

if you want to solve percent of change just do this.

1. work out the difference (increase) between the two numbers you are comparing.

2. divide the increase by the original number and multiply the answer by 100. if your answer is a negative number then this is a percentage decrease.

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