Answer to Question #252187 in Statistics and Probability for Ziyee

Question

Suppose that weekly demand for the electronic toy of a company is normally

distributed, with a mean of 2400 units and a standard deviation of 280 units.

i) What is the probability that the weekly demand for the electronic toy is

between 2350 and 2670?

ii) What is the value of a constant k, if

P(X > k) = 0.70

Answer 1

i)

$$P(2350<X<2670)=P(X<2670)-P(X\leq2350)$$

$$=P(Z<\dfrac{2670-2400}{280})-P(Z\leq\dfrac{2350-2400}{280})$$

$$\approx P(Z<0.9642857)-P(Z\leq-0.1785714)$$

$$\approx0.8325486-0.4291371\approx0.403412$$

ii)

$$P(X>k)=1-P(X\leq k)$$

$$=1-P(Z\leq\dfrac{k-2400}{280})=0.7$$

$$P(Z\leq\dfrac{k-2400}{280})=0.3$$

$$\dfrac{k-2400}{280}\approx-0.5244005$$

$$k\approx2253$$