Normal Distribution

A part, produced in high volumes, is dimensioned as shown. The machining process making this part is known to be statistically in control based on sampling data. The sampling data...

Robot Ltd. wishes to maintain enough safety stock during the lead time period between starting a new production run and its completion such that the probability of satisfying the c...

Activities A, B, C and D form the critical path for a project with a PERT network. The means and variances of the activity duration for each activity are given below. All activity...

The lengths of a large stock of titanium rods follow a normal distribution with a mean ($\mu$) of 440 mm and a standard deviation ($\sigma$) of 1 mm. What is the percentage of rods...

Let X1, X2 be two independent normal random variables with means μ1, μ2 and standard deviations σ1, σ2, respectively. Consider Y = X1 – X2; μ1 = μ2 =1, σ1 = 1, σ2 = 2. Then,

A nationalized bank has found that the daily balance available in its savings accounts follows a normal distribution with a mean of Rs. $$500$$ and a standard deviation of Rs. $$50...

Let $$X$$ be a normal random variable with mean $$1$$ and variance $$4.$$ The probability $$P\left\{ {X < 0} \right\}$$ is

A project consists of three parallel paths with mean durations and variances of $$(10,4), (12,4)$$ and $$(12,9)$$ respectively. According to the standard $$PERT$$ assumptions, the...