Question

Temperatures in LA. The average daily high temperature in January in Los Angeles is 68 degrees...

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).

Homework Answers

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
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