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the burden of potato chips in a medium-measurement bag is mentioned to be 10 oz. The amount that the packaging machine puts in these baggage is believed to have a traditional model with a mean of oz and a standard deviation of oz.. (round to four decimal areas as necessary.)
a) What fraction of all luggage bought are underweight?
b) one of the vital chips are offered in "discount packs" of 33 baggage. what's the chance that none of the 33 is underweight?
c) what's the chance that the mean weight of the 33 bags is under the cited amount?
d) what's the chance that the mean weight of a 20-bag case of potato chips is beneath 10 oz.?average Distribution:
A random variable X is asserted 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 \space \sim \space N(\mu,\frac\sigma^2n). /eq
general distribution is given with the aid of gauss and at first it is used for modeling the error .
It is assumed that all the herbal phenomenon follows usual distribution.answer and rationalization:
it's given that medium measurement chips is of 10 ounces
The quantity that packaging machine put comply with typical distribution with suggest and commonplace deviation
eq\mu= \\ \sigma= /eq
a) what fraction of luggage are underweight less than 10 ounces
So we need to locate zscore after which the use of NORMSDIST (z) characteristic of MS Excel we will get the probability
eqP(X <10)=P(Z<\ /eq
b) P(None is underweight)=?
None is underweight capability all 33 don't seem to be beneath 10 ounces
Let y denotes variety of underweight
P(None is underweight)=P(Y=0)=?
c) here n=33
So we know that eq\bar x \sim N(\mu ,\frac\sigma^2n) /eq
for this reason eq\bar x /eq observe average distribution with mean and commonplace deviation
eqP(\bar x <10)=P(Z<\ /eq
d) in a similar way right here n=20
for that reason eq\bar x /eq follow common distribution with imply and typical deviation
eqP(\bar x <10)=P(Z<\ /eq