Q.For the same shop (mean ₹5,000, standard deviation ₹800), find the probability that daily sales lie between ₹4,200 and ₹5,800. (Area between Z = 0 and Z = 1.00 is 0.3413.)

Any normally distributed variable $X$ with mean $\mu$ and standard deviation $\sigma$ can be converted to the standard normal variate $Z = \dfrac{X-\mu}{\sigma}$, which always has mean $0$ and standard deviation $1$. This lets a single, universal standard normal table — listing the area under the curve between $Z=0$ and any positive $Z$ — answer probability questions for every normal distribution, regardless of its own $\mu$ and $\sigma$. Because the curve is symmetric, the table area for $-z$ equals the area for $+z$, and the total area on either side of the mean is $0.5$. Reading a probability from a business problem is a three-step process: con …