Answer to Question #252187 in Statistics and Probability for Ziyee

Question #252187

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


1
Expert's answer
2021-10-19T03:07:16-0400

i)


P(2350<X<2670)=P(X<2670)P(X2350)P(2350<X<2670)=P(X<2670)-P(X\leq2350)

=P(Z<26702400280)P(Z23502400280)=P(Z<\dfrac{2670-2400}{280})-P(Z\leq\dfrac{2350-2400}{280})

P(Z<0.9642857)P(Z0.1785714)\approx P(Z<0.9642857)-P(Z\leq-0.1785714)

0.83254860.42913710.403412\approx0.8325486-0.4291371\approx0.403412


ii)


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

=1P(Zk2400280)=0.7=1-P(Z\leq\dfrac{k-2400}{280})=0.7

P(Zk2400280)=0.3P(Z\leq\dfrac{k-2400}{280})=0.3

k24002800.5244005\dfrac{k-2400}{280}\approx-0.5244005

k2253k\approx2253


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