0
$\begingroup$

The number of transactions handled by a bank teller in a day is a random variable with a mean of 80 and standard deviation of 5.

What can be said that the teller will handle at least 400 transactions in a day?

What can be said about the probability that the teller will handle between 70 and 90 transactions in a day?

  • 1
    Read about the _Markov_ inequality which says that the probability that a nonnegative random variable $X$ takes on values $\alpha$ or larger is bounded above by $\mu/\alpha$ where $\mu$ is the mean of $X$. Similarly, read about the _Chebyshev_ inequality which bounds the probability that $X$ differs from its mean $\mu$ by $\alpha$ or more in terms of the standard deviation.2012-10-07

2 Answers 2

0

The probability that the teller will handle at least 400 transactions in a day is the following. $P(|X| \ge 400) \le \frac{80}{400} = \frac{1}{5}$

The probability that the teller will handle between 70 and 90 transactions in a day is the following. $P(70 < X < 90) \ge 1-\frac{5^2}{100} = \frac{3}{4}$

  • 1
    $90+60 = 2*80$ Try again. My calculator says that $90+60=2*75$.2012-10-10
0

the probability that the teller will handle at least 400 transactions per day is close to 0, Im 95% confident that the teller will handle between 70 to 90 transactions in a day.

  • 0
    @DilipSarwate had the distribution been normal, i'd have been right?2012-10-07