2. The expected daily maximum temperature in the Dallas Forth area varies with s

Question

2. The expected daily maximum temperature in the Dallas Forth area varies with season. The table below shows average daily temperatures and standard deviations for the different seasons (Data from NowDATA at noaa gov) Table 1. DFW Seasonal Mean Daily Temperatures Seasonal Temperatures °F Spring Summe Winter Mean Daily Standard Deviation 48 67 14 84 79 What would be the probability thata a) mean daily fall temperature falls in the interval 69 88? b) mean daily summer temperature falls in the interval 74-95? c) mean daily winter temperature falls in the interval 56- 62? d) mean daily spring temperature falls in the interval 36- 60 F? e) mean daily winter temperature is less than 27°F?

Explanation / Answer

as z score =(X-mean)/std deviaiton

a) P(69<X<88)=P((69-79)/7<Z<(88-79)/7)=P(-1.4286<Z<1.2857)=0.9007-0.0766 =0.8242

b) P(74<X<95)=P(-1.6667<Z<1.8333)=0.9666-0.0478 =0.9188

c)P(56<X<62) =P(1<Z<1.75)=0.9599-0.8413 =0.1186

d)P(36<X<60)=P(-2.213<Z<-0.5)=0.3085-0.0134 =0.2951

e) P(X<27)=P(Z<-2.625)=0.0043

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