Question

Temperatures in LA. The average daily high temperature in January in Los Angeles is 68 degrees Fahrenheit with a standard deviation of 5 degrees Fahrenheit. Suppose that the temperatures in January closely follow a normal distribution. Round calculated answers to 4 decimal places.

1. What is the probability of observing an 76 degrees Fahrenheit temperature or higher in Los Angeles during a randomly chosen day in January?

2. How cold are the coldest 20% of the days during January in Los Angeles?  or less.

We use the following equation to convert degrees Fahrenheit to degrees Celsius:

?=(?−32)∗5/9C=(F−32)∗5/9

3. Write the probability model for the distribution of temperature in degrees Celsius in month in Los Angeles. Note: To calculate the new standard deviation, just multiply by 5/9, do not subtract 32. N(   ,  )

4. What is the probability of observing a 24.444 degrees Celsius (which roughly corresponds to 76 degrees Fahrenheit) temperature or higher in January in Los Angeles? Calculate using the degrees Celsius model from part (3).

Answer 1

1_)

for normal distribution z score =(X-μ)/σ
here mean=       μ=	68
std deviation   =σ=	5.0000

probability of observing an 76 degrees Fahrenheit temperature or higher in Los Angeles during a randomly chosen day in January:

probability =P(X>76)=P(Z>(76-68)/5)=P(Z>1.6)=1-P(Z<1.6)=1-0.9452=0.0548

2)

for 20th percentile critical value of z=		-0.842
therefore corresponding value=mean+z*std deviation=			63.7919 or less

3)

mean =(68-32)*5/9 =20

standard deviation =5*5/9 =2.7778

probability model ~ N(20 , 2.7778)

4_)

probability =P(X>24.444)=P(Z>(24.444-20)/2.778)=P(Z>1.6)=1-P(Z<1.6)=1-0.9452=0.0548