ifference between the forecast maximum temperature and the actual maximum temper
ID: 3362223 • Letter: I
Question
ifference between the forecast maximum temperature and the actual maximum temperature (in degrees Celsius) in a city is Normally distributed with mean 0and standard d eviation 1.2 a. Find the probability thatthe actual maxium is within 1.0 degrees ofthe forecast masimum b. Which is more likely: an underestimate of0.5 degrees or more, or a forecast within O0.5 degreesof the actual maximum? A reporteris writing up this infomation for an article about weather forecasts, and wants a sensationalis tangle, soshe asks: 'How bad can it get? Let's say, on the lowside, the most extreme 1% ofdifferences are in what range? And what about the worst 1% on the high side?" c.Explanation / Answer
a) probability =P(-1<X<1) =P((-1-0)/12<Z<(1-0)/12)=0.5332-0.4668 =0.0664
b)probability of forecast with in 0.5 =P(-0.5<X<00.5) =P((-0.5-0)/12<Z<(0.5-0)/12)=P(-0.0417<Z<0.0417)
=0.5166-0.4834 =0.0332
probability of underestiate of 0.5 or more =P(X<-0.5)=P(Z<-0.417)=0.4834
from above underestiate of 0.5 or more is more likely.
c)for lowest 1% ; critical z score = -2.326
therfore low side temperature differnence =mean+z*std deviation =0-2.326*12=-30.91
for high side 1% ; critical z score =2.326
therfore high side temperature differnence =mean+z*std deviation =0+2.326*12=30.91
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