Use the information in
[link] to answer the following questions.
Find the 30
th percentile, and interpret it in a complete sentence.
What is the probability that the age of a randomly selected smartphone user in the range 13 to 55+ is less than 27 years old.
Let
X = a smart phone user whose age is 13 to 55+.
X ~
N (36.9, 13.9)
To find the 30
th percentile, find
k such that
P (
x <
k ) = 0.30.
invNorm(0.30, 36.9, 13.9) = 29.6 years
Thirty percent of smartphone users 13 to 55+ are at most 29.6 years and 70% are at least 29.6 years.
Find
P (
x <27)
normalcdf(0,27,36.9,13.9) = 0.2342
(Note that normalcdf(–10
99 ,27,36.9,13.9) = 0.2382. The two answers differ only by 0.0040.)
There are approximately one billion smartphone users in the world today. In the United States the ages 13 to 55+ of smartphone users approximately follow a normal distribution with approximate mean and standard deviation of 36.9 years and 13.9 years respectively. Using this information, answer the following questions (round answers to one decimal place).
Two thousand students took an exam. The scores on the exam have an approximate normal distribution with a mean
μ = 81 points and standard deviation
σ = 15 points.
Calculate the first- and third-quartile scores for this exam.
The middle 50% of the exam scores are between what two values?
A citrus farmer who grows mandarin oranges finds that the diameters of mandarin oranges harvested on his farm follow a normal distribution with a mean diameter of 5.85 cm and a standard deviation of 0.24 cm.
a. Find the probability that a randomly selected mandarin orange from this farm has a diameter larger than 6.0 cm. Sketch the graph.
