Answer:
The temperature that separates the lowest 59.5% of temperatures from the rest is 83.66 degrees Fahrenheit.
Step-by-step explanation:
Mean temperature = u = 77.9
Standard Deviation = [tex]\sigma[/tex] = 2.4
Since the distribution is normal and we have the value of population standard deviation, we will use the concept of z-score to find the desired value.
We have to find the value that separates lowest 59.5% of the temperature from the rest. This means our desired value is above 59.5% of the data values.
From the z-table we can find a z-score which is above 59.5% of the values and then convert it to its equivalent temperature using the formula.
From the z-table, the z-score which is above 59.5% of the value is:
z = 0.24
The formula for z-score is:
[tex]z=\frac{x-\mu}{\sigma}[/tex]
Using the values we have:
[tex]0.24=\frac{x-77.9}{2.4}\\\\ 5.76=x-77.9\\\\ x=83.66[/tex]
This is our data value equivalent to a z-score of 0.24. Just like 59.5% of z values were below 0.24, in the same manner, 59.5% of temperatures are below 83.66 degrees Fahrenheit.
Therefore, the temperature that separates the lowest 59.5% of temperatures from the rest is 83.66 degrees Fahrenheit.
