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.