Question

The average daily sales of 700 branch office was rs 120 thousands and the standard deviation is rs 15,000 during the distribution to be normal how many branch have sale

Answer 1

Assuming the distribution to be normal indicate how many branches have sales between 1. Rs. 90 thousands and Rs 115 thoudands

Given $\mu=120 \ thousands, \sigma=15 \ thousands$

$$P(90<X<115)=P(X<115)-P(X\leq 90)$$

$$=P(Z<\dfrac{115-120}{15})-P(Z\leq \dfrac{90-120}{15})$$

$$\approx P(Z<-0.3333)-P(Z\leq -2)$$

$$\approx0.36944-0.02275\approx0.3467$$

$$0.3467(700)=243$$

243 branches have sales between $Rs.90,000$ and $Rs.115,000.$

2. Rs. 110 thousands and Rs 135 thoudands

Given $\mu=120 \ thousands, \sigma=15 \ thousands$

$$P(110<X<135)=P(X<135)-P(X\leq 110)$$

$$=P(Z<\dfrac{135-120}{15})-P(Z\leq \dfrac{110-120}{15})$$

$$\approx P(Z<1)-P(Z\leq -0.6667)$$

$$\approx0.84134-0.25249\approx0.5889$$

$$0.5889(700)=412$$

412 branches have sales between $Rs.110,000$ and $Rs.135,000.$