A bag of cookies is underweight if it weighs less than 500 grams The filling process dispenses cookies with weight that follows the normal distribution with mean 510 grams and standard deviation 4 grams a What is the probability that a randomly selected bag is underweight? b If you randomly select 5 bags, what is the probability that exactly 2 of them will be underweight?

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Answer:- a) Given data,Weight less than =500 grams [under weight]Normat distribution with mean =510 gramsstandard deviation =4 grams\rightarrow The probability that a ganctomly getected bag is underweight\begin{array}{l}P[x<500]=P\left[z<\frac{500-510}{4}\right] \\=P\left[z<\frac{-10}{4}\right] \\=P[z<-2.5] \\\begin{array}{l}\text { 4) } 10(2.5 \\\frac{8}{20} \\\frac{20}{0}\end{array} \\.0 .0062 \\\end{array}b) The probability that Exactly 2 of them Witl be under weight\begin{aligned}P(y=2) & =\left[{ }_{5} C_{2}\right] 0.0062^{2} *[1-0.0062]^{3} \\& =0.0004\end{aligned} ...