Question

The temperature of coffee served at a restaurant is normally distributed with an average temperature of 160 degrees Fahrenheit and a standard deviation of 5.4 degrees Fahrenheit. What is the coffee temperature for the 20th percentile? Enter your answer to four decimal places.

Answer 1

Answer:

The 20th percentile of coffee temperature is 155.4532 degrees Fahrenheit.  

Step-by-step explanation:

We are given the following information in the question:

Mean, μ = 160 degrees

Standard Deviation, σ = 5.4 degrees

We are given that the distribution of temperature of coffee is a bell shaped distribution that is a normal distribution.

Formula:

$z_{score} = \displaystyle\frac{x-\mu}{\sigma}$

We have to find the value of x such that the probability is 0.2

$P( X < x) = P( z < \displaystyle\frac{x - 160}{5.4})=0.2$  

Calculation the value from standard normal z table, we have,  

$\displaystyle\frac{x - 160}{5.4} = -0.842\\\\x = 155.4532$  

Thus,

$P_{20}=155.4532$

The 20th percentile of coffee temperature is 155.4532 degrees Fahrenheit.