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:
[tex]z_{score} = \displaystyle\frac{x-\mu}{\sigma}[/tex]
We have to find the value of x such that the probability is 0.2
[tex]P( X < x) = P( z < \displaystyle\frac{x - 160}{5.4})=0.2[/tex]
Calculation the value from standard normal z table, we have,
[tex]\displaystyle\frac{x - 160}{5.4} = -0.842\\\\x = 155.4532[/tex]
Thus,
[tex]P_{20}=155.4532[/tex]
The 20th percentile of coffee temperature is 155.4532 degrees Fahrenheit.
