Question

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

1. What is the probability of observing an 71 degrees Fahrenheit temperature or higher in Los Angeles during a randomly chosen day in December?

2. How cold are the coldest 15% of the days during December in Los Angeles?  or less.

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

C=(F−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 21.667 degrees Celsius (which roughly corresponds to 71 degrees Fahrenheit) temperature or higher in December in Los Angeles? Calculate using the degrees Celsius model from part (3).

Answer 1

Given Information:

Let F denotes the daily high temperature in Fahrenheit in December in Los Angeles.

1. The probability of observing an 71 degrees Fahrenheit temperature or higher in Los Angeles during a randomly chosen day in December is calculated using standard normal table and is given by:

Hence, the probability of observing an 71 degrees Fahrenheit temperature or higher in Los Angeles during a randomly chosen day in December is 0.2743.

2. To calculate how cold are the coldest 15% of the days during December in Los Angeles percentile is used.

Let the temperature in Fahrenheit of the coldest 15% of days be denoted by M.

The value of M is calculated using inverse standard normal table and is given by:

The coldest 15% of the days during December in Los Angeles or less has a temperature of 62.818 degrees Fahrenheit or less.

The following equation is used to convert degrees Fahrenheit to degrees Celsius:

.

The expected temperature in Celsius is given by:

The standard deviation of temperature in Celsius is given by:

3.The probability model for the distribution of temperature in degrees Celsius in month in Los Angeles is given by:

4. The probability of observing a 21.667 degrees Celsius temperature or higher in Los Angeles during a randomly chosen day in December is calculated using standard normal table and is given by:

Hence, the probability of a 21.667 degrees Celsius temperature or higher in Los Angeles during a randomly chosen day in December is 0.2743.