The weight of a sophisticated running shoe is normally distributed with a mean of 340g and a variance of 200 g2.

(a) What is the probability that a shoe weighs more than 370g? (0.0169)

(b) What must the standard deviation of weight be in order for the company to state that 99.9% of its shoes are less than 370g? (94,28 g2)

(c) If the variance remains at 200 g2, what must the mean weight be in order for the company to state that 99.9% of its shoes are less than 370g? (326,4 g)

Thispastyear,anelementaryschoolbeganusinganewmethodtoteacharithmetictofirstgraders.Astandardizedtest,administeredattheendoftheyear,wasusedtomeasuretheeffectivenessofthenewmethod.Thedistributionofpastscoresonthestandardizedtestproducedameanof75andastandarddeviationof10.

a)Ifthenewmethodisnodifferentfromtheoldmethod,whatistheapproximateprobabilitythatthemeanscoreof36studentswillbegreaterthan79?

b)Whatassumptionsmustbesatisfiedtomakeyouranswervalid?