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the load of potato chips in a medium-dimension bag is mentioned to be 10 oz.. The quantity that the packaging computing device places in these bags is believed to have a normal mannequin with an average of oz. and a typical deviation of oz. (circular to 4 decimal areas as necessary.)

a) What fraction of all luggage bought are underweight?

b) one of the crucial chips are sold in "bargain packs" of 33 baggage. what's the chance that not one of the 33 is underweight?

c) what is the chance that the suggest weight of the 33 bags is under the mentioned volume?

d) what's the likelihood that the mean weight of a 20-bag case of potato chips is under 10 oz.?

ordinary Distribution:A random variable X is said to be following common distribution with meaneq\mu /eq and variance eq\sigma^2 /eq if its distribution is given as eqf(x|\mu,\sigma^2)=\frac1\sqrt2\pi \sigma^2e^-\frac(x-\mu)^22\sigma^2 \qquad , -\infty \leq X \leq \infty \\ \bar x \area \sim \house N(\mu,\frac\sigma^2n). /eq

general distribution is given by way of gauss and at the beginning it's used for modeling the error .

It is assumed that all the natural phenomenon follows standard distribution.

answer and rationalization:it's given that medium size chips is of 10 ounces

The volume that packaging computer put observe standard distribution with suggest and standard deviation

eq\mu= \\ \sigma= /eq

**a)** what fraction of baggage are underweight under 10 oz

So we need to locate zscore and then the usage of NORMSDIST (z) feature of MS Excel we can get the likelihood

eqP(X <10)=P(Z<\ /eq

**b)** P(None is underweight)=?

None is underweight skill all 33 aren't under 10 oz.

Let y denotes variety of underweight

y ~Binom(33,

P(None is underweight)=P(Y=0)=?

eqP(Y=0)=\ /eq

**c)** right here n=33

So we comprehend that eq\bar x \sim N(\mu ,\frac\sigma^2n) /eq

for that reason eq\bar x /eq comply with commonplace distribution with mean and average deviation

eqP(\bar x <10)=P(Z<\ /eq

**d)** in a similar fashion here n=20

for this reason eq\bar x /eq observe general distribution with suggest and commonplace deviation

eqP(\bar x <10)=P(Z<\ /eq