Activity A Activity B Optimistic time ($t_o$) = 4 days Optimistic time ($t_o$) = 4 days Most likely time ($t_l$) = 7 days Most likely time ($t_l$) = 6 days Pessimistic time ($t_p$) = 16 days Pessimistic time ($t_p$) = 22 days
PERT Standard Deviation Calculation
The standard deviation for project activities is calculated using the PERT (Program Evaluation and Review Technique) formula, which estimates the dispersion of activity durations.
The formula for standard deviation ($\sigma$) is:
$ \sigma = \frac{t_p - t_o}{6} $
Where:
- $t_p$ = Pessimistic time estimate
- $t_o$ = Optimistic time estimate
Activity A Standard Deviation
Given values for Activity A:
- Optimistic time ($t_o$) = 4 days
- Pessimistic time ($t_p$) = 16 days
Calculation:
$ \sigma_A = \frac{16 \text{ days} - 4 \text{ days}}{6} = \frac{12 \text{ days}}{6} = 2 \text{ days} $
Activity B Standard Deviation
Given values for Activity B:
- Optimistic time ($t_o$) = 4 days
- Pessimistic time ($t_p$) = 22 days
Calculation:
$ \sigma_B = \frac{22 \text{ days} - 4 \text{ days}}{6} = \frac{18 \text{ days}}{6} = 3 \text{ days} $
Conclusion
The standard deviation for Activity A is 2 days, and the standard deviation for Activity B is 3 days.
Important Questions from Basics of Probability
Suppose a 5-bit message is transmitted from a source to a destination through a noisy channel. The probability that a bit of the message gets flipped during transmission is 0.01. Flipping of each bit is independent of one another. The probability that the message is delivered error-free to the destination is ______ . (rounded off to three decimal places)
- A quadratic polynomial $(x - \alpha)(x - \beta)$ over complex numbers is said to be square invariant if $(x - \alpha)(x - \beta) = (x - \alpha^2)(x - \beta^2)$. Suppose from the set of all square invariant quadratic polynomials we choose one at random.
The probability that the roots of the chosen polynomial are equal is ____________ (rounded off to one decimal place) - If, out of 50 fish of a pond, 12 had no ectoparasite and remaining had varying numbers of parasites on them, then how many of fish had at least one parasite ?
For a distribution with mean, median, mode and standard deviation 25, 24, 26 and 5 respectively, Karl Pearson's coefficient of skewness equals to:
Suppose two distributions have the same mean, same standard deviation and are equally skewed, but the first distribution is more peaked than the
other. This feature of the frequency distributions in which they are different are called:
