<< Chapter < Page Chapter >> Page >

Try it

Use the information in [link] to answer the following questions.

  1. Find the 30 th percentile, and interpret it in a complete sentence.
  2. 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)

  1. 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.
  2. Find P ( x <27)
    This is a normal distribution curve. The peak of the curve coincides with the point 36.9 on the horizontal axis. The point 27 is also labeled. A vertical line extends from 27 to the curve. The area under the curve to the left of 27 is shaded. The shaded area shows that P(x < 27) = 0.2342.

    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.)
Got questions? Get instant answers now!

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).

a. Calculate the interquartile range ( IQR ).

a.

  • IQR = Q 3 Q 1
  • Calculate Q 3 = 75 th percentile and Q 1 = 25 th percentile.
  • invNorm(0.75,36.9,13.9) = Q 3 = 46.2754
  • invNorm(0.25,36.9,13.9) = Q 1 = 27.5246
  • IQR = Q 3 Q 1 = 18.7508

Got questions? Get instant answers now!

b. Forty percent of the ages that range from 13 to 55+ are at least what age?

b.

  • Find k where P ( x > k ) = 0.40 ("At least" translates to "greater than or equal to.")
  • 0.40 = the area to the right.
  • Area to the left = 1 – 0.40 = 0.60.
  • The area to the left of k = 0.60.
  • invNorm(0.60,36.9,13.9) = 40.4215.
  • k = 40.42.
  • Forty percent of the ages that range from 13 to 55+ are at least 40.42 years.

Got questions? Get instant answers now!
Got questions? Get instant answers now!

Try it

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.

  1. Calculate the first- and third-quartile scores for this exam.
  2. The middle 50% of the exam scores are between what two values?
  1. Q 1 = 25 th percentile = invNorm(0.25,81,15) = 70.9
    Q 3 = 75 th percentile = invNorm(0.75,81,15) = 91.9
  2. The middle 50% of the scores are between 70.9 and 91.1.
Got questions? Get instant answers now!

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.

a. normalcdf(6,10^99,5.85,0.24) = 0.2660

This is a normal distribution curve. The peak of the curve coincides with the point 2 on the horizontal axis. The values 1.8 and 2.75 are also labeled on the x-axis. Vertical lines extend from 1.8 and 2.75 to the curve. The area between the lines is shaded.
Got questions? Get instant answers now!

b. The middle 20% of mandarin oranges from this farm have diameters between ______ and ______.

b.

  • 1 – 0.20 = 0.80
  • The tails of the graph of the normal distribution each have an area of 0.40.
  • Find k1 , the 40 th percentile, and k2 , the 60 th percentile (0.40 + 0.20 = 0.60).
  • k1 = invNorm(0.40,5.85,0.24) = 5.79 cm
  • k2 = invNorm(0.60,5.85,0.24) = 5.91 cm

Got questions? Get instant answers now!

c. Find the 90 th percentile for the diameters of mandarin oranges, and interpret it in a complete sentence.

c. 6.16: Ninety percent of the diameter of the mandarin oranges is at most 6.15 cm.

Got questions? Get instant answers now!
Got questions? Get instant answers now!

Try it

Using the information from [link] , answer the following:

  1. The middle 45% of mandarin oranges from this farm are between ______ and ______.
  2. Find the 16 th percentile and interpret it in a complete sentence.
  1. The middle area = 0.40, so each tail has an area of 0.30.

    1 – 0.40 = 0.60

    The tails of the graph of the normal distribution each have an area of 0.30.

    Find k1 , the 30 th percentile and k2 , the 70 th percentile (0.40 + 0.30 = 0.70).

    k1 = invNorm(0.30,5.85,0.24) = 5.72 cm

    k2 = invNorm(0.70,5.85,0.24) = 5.98 cm

  2. normalcdf(5,1099,5.85,0.24) = 0.9998
Got questions? Get instant answers now!

Questions & Answers

you are working for a bank.The bank manager wants to know the mean waiting time for all customers who visit this bank. she has asked you to estimate this mean by taking a sample . Briefly explain how you will conduct this study. assume the data set on waiting times for 10 customers who visit a bank. Then estimate the population mean. choose your own confidence level.
Halpha Reply
what marriage for 10 years
Ambaye Reply
fit a least square model of y on x ? what is the regression coefficient ? x : 2 3 6 8 9 10 y : 5 6 7 10 8 11
Nayab Reply
how can we find the expectation of any function of X?
Jennifer
I've been using this app for some time now. I'm taking a stats class in college in spring and I still have no idea what's going on. I'm also 55 yrs old. Is there another app for people like me?
Tamala
Serious
Hamza
yes I am. it's been decades since I've been in school.
Tamala
who are u
zaheer
is there a private chat we can do
Tamala
hello how can I get PDF of solutions introduction mathematical statistics ( fourth education) who can help me
ahssal
can anyone help me
Halim
what is probability
zaheer Reply
simply probability means possibility.. definition:Probability is a measure of the likelihood of an event to occur.
laraib
fit a least square model of y on x ? what is the regression coefficient ? x : 2 3 6 8 9 10 y : 5 6 7 10 8 11
Nayab
classification of data by attributes is called
Yamin Reply
qualitative classification
talal
tell me details about measure of Dispersion
Halim
Following data provided Class Frequency less than 10 10-20 5 15 10-30 25 12 40 and above Which measure of central tendency would you compute and why?
Nija Reply
a box contains a few red and a few blue balls.one ball is drawn randomly find the probability of getting a red ball if we know that there are 30 red and 40 blue balls in the box
harish Reply
3/7
RICH
Total=30+40=70 P(red balls) =30/70 Therefore the answer is 3/7
Anuforo
define transport statistical unit
Dennis Reply
describe each transport statistical unit
Dennis
explain uses of each transport statistical unit
Dennis
identify various transport statistical units with their example
Dennis
I didn't understand about Chi- square.
Esayas Reply
explain the concept of data analysis and data processing
Kim Reply
the following data represent the number of pop up advertisement received by 10 families during the past month.calculate the mean number of advertisement received by each family during month.43,37,35,30,41,23,33,31,16,21
ejaz Reply
mean=43+37+35+30+41+23+33+31+16/10 =310/10 =31
Anuforo
43+37+35+30+41+23+33+31+16 divided by 10 =310/10 =31
Anuforo
=310/10 =31
Anuforo
the following data represent the number of pop up advertisement received by 10 families during the past month.calculate the mean number of advertisement received by each family during month.43,37,35,30,41,23,33,31,16,21
ejaz Reply
In a recent survey of nurses in Region II, it was found out that the average monthly net income of nurses is Php 8,048.25. Suppose a researcher wants to test this figure by taking a random sample of 158 nurses in Region II to determine whether the monthly income has changed. Supposed further that th
Sweet Reply
what is index number
Mir Reply
Suppose from the 1,000 freshmen that took the entrance examination, it was found out that the standard deviation was 10 a. How many students passed the test if the passing score is set 75? b. What scores comprise the middle 95% of all scores?
Sweet Reply
Hi
HAYATUL
can you answer my question.
Sweet

Get Jobilize Job Search Mobile App in your pocket Now!

Get it on Google Play




Source:  OpenStax, Introductory statistics. OpenStax CNX. May 06, 2016 Download for free at http://legacy.cnx.org/content/col11562/1.18
Google Play and the Google Play logo are trademarks of Google Inc.

Notification Switch

Would you like to follow the 'Introductory statistics' conversation and receive update notifications?

Ask