Section 5.3: Normal Distributions: Finding Values

Answer the questions about the specified normal distribution.

Q1: The lifetime of ZZZ batteries are normally distributed with a mean of 265 hours and a standard deviation ó of 10 hours. Find the number of hours that represent the the 25th percentile.

A1:
x = µ + zó
= 265 + -0.608 (10)
= 271.08

Q2: Scores on an English placement test are normally distributed with a mean of 36 and standard deviation ó of 6.5. Find the score that marks the top 10%.

Q2:
x = µ + zó
= 36 + -1.208 (6.5)
= 28.15

Instead of tables I use this applet

http://davidmlane.com/hyperstat/z_table.html

When you say 25 percentile, doesn't that mean that 25% of the date is below?
Your answer of 271 is above the mean, therefore more than the 50% percentile.

using the second part , entering 365 for mean, and 10 DV, I entered .25 for "shaded area" and clicked on below to get 358.25

similarly for your second, doesn't top 10% mean that 90% are below??
so enter mean=36 sd=10 .9 for shade and click below to get 48.8

(how could your score of 28.15, which is well below the average of 36 put somebody in the top 10% ?)

A survey was conducted to measure the number of hours per week adults spend on home

computers. In the survey, the number of hours was normally distributed, with a mean of 8
hours and a standard deviation of 1 hour. A survey participant is randomly selected. Find
the probability that the hours spent on the home computer by the participant are between
5.5 and 9.5 hours per week.

Q2: The score that marks the top 10% is approximately 28.15.

To find the score that marks the top 10%, you need to use the formula x = µ + zó.

Step 1: Identify the given values:
- Mean (µ) = 36
- Standard deviation (ó) = 6.5

Step 2: Find the z-score corresponding to the given percentile. Since we want the top 10%, we need to find the z-score that corresponds to the area to the left of 90% in the standard normal distribution.

You can find this value using a standard normal distribution table or a calculator. For example, using a calculator, the z-score for the 90th percentile is approximately -1.28.

Step 3: Plug in the values into the formula x = µ + zó:
x = 36 + (-1.28)(6.5)
x = 36 - 8.32
x ≈ 28.15

Therefore, the score that marks the top 10% is approximately 28.15.