Question

A normal random variable with mean and standard deviationboth equal to 10 degrees Celsius. What is the probability that the temperature at a randomly chosen time will be less than or equal to 59 degrees Fahrenheit?

Answer 1

0.57142

Explanation:

A normal random variable with mean and standard deviation both equal to 10 degrees Celsius. What is the probability that the temperature at a randomly chosen time will be less than or equal to 59 degrees Fahrenheit?

We are told that the Mean and Standard deviation = 10°C

We convert to Fahrenheit

(10°C × 9/5) + 32 = 50°F

Hence, we solve using z score formula

z = (x-μ)/σ, where

x is the raw score = 59 °F

μ is the population mean = 50 °F

σ is the population standard deviation = 50 °F

z = 59 - 50/50

z = 0.18

Probability value from Z-Table:

P(x ≤59) = 0.57142

The probability that the temperature at a randomly chosen time will be less than or equal to 59 degrees Fahrenheit

is 0.57142