The average daily temperature in October in Boston is 61°F with a standard devia

Question

The average daily temperature in October in Boston is 61°F with a standard deviation of 5°F. These temperatures closely follow a normal distribution. of a normal distributionard What is the probability of observing a 67°F temperature or higher in Boston during a randomly chosen day in October? How warm are the hottest 20% of the days (days with highest average high tempera- ture) during October in Boston? We use the following equation to convert (Fahrenheit) to °C (Celsius): 5 C= (F-32) Write the probability model for the distribution of temperature in °C in October in Boston What is the probability of observing a 20°C (which roughly corresponds to 68°F) tem- perature or higher in October in Boston? Calculate using the °C model from question 4 Estimate the IQR of the temperatures (in °C) in October in Boston

Explanation / Answer

a)probabiliy of observing 67 degree or higher =P(X>67)=P(Z>67-61)/5)=P(Z>1.2)=0.1151

b) for hottest 20% ;at 80th percentile z =0.8416

hence corresponding value =mean +z*std deviation =67+0.8416*5=71.21

c) C follows normal distribution with

mean =(5/9)*(67-32)=19.44

and std deviation =(5/9)*5=2.78

probability of 20 degree celsius or higher =P(X>20)=P(Z>(20-19.44)/2.78)=P(Z>(0.2)=0.4207

for 1st and 3rd quartile z =-/+ 0.6475

hence interquartile range =2*0.6745*std deviation =2*0.6745*2.78 =3.7472 ~ 3.75 oC

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