Question

for all of the normal distribution percentages (probabilities). you need to use the methods shown in class, which requires using a standard normal probability table. if you use technology to do these calculations for you, there might be rounding issues which will mark your answers as incorrect.
if you need a copy of the table, you can find it on this website table a - standard normal probabilities
body temperatures: most people think that the normal adult body temperature is 98.6 degrees fahrenheit. that figure, based on a 19th century study, has recently been challenged. a more recent figure is 98.1 degrees. the standard deviation appears to be around 0.7 degrees and the distribution is approximately normal.
a) based on this model, below what body temperature are the coolest 10% of all people?
degrees (round your answer to 1 decimal place)
b) based on this model, above what body temperature are the hottest 30% of all people?
degrees (round your answer to 1 decimal place)
question help: message instructor

Explanation:

Step1: Find z - scores

For part A (coolest 10%):
The z - score corresponding to the left - tail area of \(0.10\) is \(z_{1}\). Looking up in the standard normal table, \(z_{1}\approx - 1.28\)
For part B (hottest 30%):
The area to the left is \(1 - 0.30=0.70\). Looking up in the standard normal table, \(z_{2}\approx0.52\)

Step2: Use the formula \(x=\mu+z\sigma\)

Given \(\mu = 98.1\) and \(\sigma = 0.7\)
For part A:
\(x_{1}=\mu+z_{1}\sigma=98.1+( - 1.28)\times0.7\)
\(x_{1}=98.1-0.896 = 97.204\approx97.2\)
For part B:
\(x_{2}=\mu+z_{2}\sigma=98.1 + 0.52\times0.7\)
\(x_{2}=98.1+0.364=98.464\approx98.5\)

Answer:

A. \(97.2\) degrees
B. \(98.5\) degrees