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A machine puts liquid into bottles of perfume. The amount of liquid put into each bottle,...

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Statistics

A machine puts liquid into bottles of perfume. The amount ofliquid put into each bottle, Dml, follows a normal distributionwith mean 25ml.

Given that 15% of bottles contain less than 24.63ml

a.) find, to 2 decimal places, the value of k such thatP(24.63

A random sample of 200 bottles is taken.

b.) Using a normal approximation, find the probability thatfewer than half of these bottles contain between 24.63ml and kml

The machine is adjusted so that the standard deviation of theliquid put in the bottles is now 0.16ml

Following the adjustments, Hannah believes that the mean amountof liquid put in each bottle is less than 25 ml

She takes a random sample of 20 bottles and finds the meanamount of liquid to be 24.94ml

c.) Test Hannah's belief at the 5% level of significance. Youshould state your hypothesis clearly.

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