Question

Average daily high temperatures in june in LA is 77°F with a standard deviation of 5°F. and it can be assumed that they do follow a normal distribution. We use the following equation to convert °F to °C: C=(F-32)*5/9Write the probability model for the distribution of temperature in °C in June in LA.

A) Mean = 25°C, Standard Deviation = 2.78°C

B) Mean = 25°C, Standard Deviation = 5°C

C) Mean = 77°C, Standard Deviation = 5°C

D) Mean = 77°C, Standard Deviation = 2.78°C

Answer 1

The correct probability model for the distribution of temperature in Celsius in June in Los Angeles is a normal distribution with a mean of 25°C and a standard deviation of 2.78°C after converting from Fahrenheit to Celsius.

Step-by-step explanation:

The student is asking about the probability model for the distribution of temperatures in Celsius in Los Angeles during June. Since the temperatures in Fahrenheit follow a normal distribution, after converting to Celsius, they will continue to follow a normal distribution. The mean temperature in Fahrenheit is 77°F, which when converted to Celsius using the formula C = (F - 32) * 5/9 gives us (77 - 32) * 5/9 = 25°C as the mean. The standard deviation in Fahrenheit is 5°F. When converted to Celsius, it scales with the conversion factor of 5/9, yielding a new standard deviation of 5 * 5/9 = 2.78°C. Therefore, the correct probability model for the distribution of temperature in Celsius in June in LA is option A: Mean = 25°C, Standard Deviation = 2.78°C