# 6.2 Using the normal distribution  (Page 2/25)

 Page 2 / 25

`invNorm` in `2nd DISTR` . invNorm(area to the left, mean, standard deviation)
For this problem, invNorm(0.90,63,5) = 69.4

d. Find the 70 th percentile (that is, find the score k such that 70% of scores are below k and 30% of the scores are above k ).

d. Find the 70 th percentile.

Draw a new graph and label it appropriately. k = 65.6

The 70 th percentile is 65.6. This means that 70% of the test scores fall at or below 65.5 and 30% fall at or above.

invNorm(0.70,63,5) = 65.6

## Try it

The golf scores for a school team were normally distributed with a mean of 68 and a standard deviation of three.

Find the probability that a randomly selected golfer scored less than 65.

normalcdf(10 99 ,65,68,3) = 0.1587

A personal computer is used for office work at home, research, communication, personal finances, education, entertainment, social networking, and a myriad of other things. Suppose that the average number of hours a household personal computer is used for entertainment is two hours per day. Assume the times for entertainment are normally distributed and the standard deviation for the times is half an hour.

a. Find the probability that a household personal computer is used for entertainment between 1.8 and 2.75 hours per day.

a. Let X = the amount of time (in hours) a household personal computer is used for entertainment. X ~ N (2, 0.5) where μ = 2 and σ = 0.5.

Find P (1.8< x <2.75).

The probability for which you are looking is the area between x = 1.8 and x = 2.75. P (1.8< x <2.75) = 0.5886

normalcdf(1.8,2.75,2,0.5) = 0.5886

The probability that a household personal computer is used between 1.8 and 2.75 hours per day for entertainment is 0.5886.

b. Find the maximum number of hours per day that the bottom quartile of households uses a personal computer for entertainment.

b. To find the maximum number of hours per day that the bottom quartile of households uses a personal computer for entertainment, find the 25 th percentile, k , where P ( x < k ) = 0.25.

invNorm(0.25,2,0.5) = 1.66

The maximum number of hours per day that the bottom quartile of households uses a personal computer for entertainment is 1.66 hours.

## Try it

The golf scores for a school team were normally distributed with a mean of 68 and a standard deviation of three. Find the probability that a golfer scored between 66 and 70.

normalcdf(66,70,68,3) = 0.4950

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.

a. Determine the probability that a random smartphone user in the age range 13 to 55+ is between 23 and 64.7 years old.

a. normalcdf(23,64.7,36.9,13.9) = 0.8186

b. Determine the probability that a randomly selected smartphone user in the age range 13 to 55+ is at most 50.8 years old.

b. normalcdf(–10 99 ,50.8,36.9,13.9) = 0.8413

c. Find the 80 th percentile of this distribution, and interpret it in a complete sentence.

c.

• invNorm(0.80,36.9,13.9) = 48.6
• The 80 th percentile is 48.6 years.
• 80% of the smartphone users in the age range 13 – 55+ are 48.6 years old or less.

#### Questions & Answers

what is standard deviation?
It is the measure of the variation of certain values from the Mean (Center) of a frequency distribution of sample values for a particular Variable.
Dominic
Yeah....the simplest one
IRFAN
what is the number of x
10
Elicia
Javed Arif
Jawed
how will you know if a group of data set is a sample or population
population is the whole set and the sample is the subset of population.
umair
if the data set is drawn out of a larger set it is a sample and if it is itself the whole complete set it can be treated as population.
Bhavika
hello everyone if I have the data set which contains measurements of each part during 10 years, may I say that it's the population or it's still a sample because it doesn't contain my measurements in the future? thanks
Alexander
Pls I hv a problem on t test is there anyone who can help?
Peggy
What's your problem Peggy Abang
Dominic
Bhavika is right
Dominic
what is the problem peggy?
Bhavika
hi
Sandeep
Hello
hi
Bhavika
hii Bhavika
Dar
Hi eny population has a special definition. if that data set had all of characteristics of definition, that is population. otherwise that is a sample
Hoshyar
three coins are tossed. find the probability of no head
three coins are tossed consecutively or what ?
umair
umair
or .125 is the probability of getting no head when 3 coins are tossed
umair
🤣🤣🤣
Simone
what is two tailed test
if the diameter will be greater than 3 cm then the bullet will not fit in the barrel of the gun so you are bothered for both the sides.
umair
in this test you are worried on both the ends
umair
lets say you are designing a bullet for thw gun od diameter equals 3cm.if the diameter of the bullet is less than 3 cm then you wont be able to shoot it
umair
In order to apply weddles rule for numerical integration what is minimum number of ordinates
excuse me?
Gabriel
why?
didn't understand the question though.
Gabriel
which question? ?
We have rules of numerical integration like Trapezoidal rule, Simpson's 1/3 and 3/8 rules, Boole's rule and Weddle rule for n =1,2,3,4 and 6 but for n=5?
John
geometric mean of two numbers 4 and 16 is:
10
umair
really
iphone
quartile deviation of 8 8 8 is:
iphone
sorry 8 is the geometric mean of 4,16
umair
quartile deviation of 8 8 8 is
iphone
can you please expalin the whole question ?
umair
mcq
iphone
h
iphone
can you please post the picture of that ?
umair
how
iphone
hello
John
10 now
John
how to find out the value
can you be more specific ?
umair
yes
KrishnaReddy
what is the difference between inferential and descriptive statistics
descriptive statistics gives you the result on the the data like you can calculate various things like variance,mean,median etc. however, inferential stats is involved in prediction of future trends using the previous stored data.
umair
if you need more help i am up for the help.
umair
Thanks a lot
Anjali
Inferential Statistics involves drawing conclusions on a population based on analysis of a sample. Descriptive statistics summarises or describes your current data as numerical calculations or graphs.
fred
my pleasure😊. Helping others offers me satisfaction 😊
umair
for poisson distribution mean............variance.
both are equal to mu
Faizan
mean=variance
Faizan
what is a variable
something that changes
Festus
why we only calculate 4 moment of mean? asked in papers.
why we only 4 moment of mean ? asked in BA exam
Faizan
Good evening, can you please help me by sharing regression and correlation analysis notes....thank you in advance
Hello, can you please share the possible questions that are likely to be examined under the topic: regression and correlation analysis.
Refiloe
for normal distribution mean is 2 & variance is 4 find mu 4?
repeat quastion again
Yusuf
find mu 4. it can be wrong but want to prove how.
Faizan
for a normal distribution if mu 4 is 12 then find mu 3?
Question hi wrong ha
Tahir
ye BA mcqs me aya he teen he. 2dafa aya he
Faizan
if X is normally distributed. (n,b). then its mean deviation is?
Faizan
The answer is zero, because all odd ordered central moments of a normal distribution are Zero.
nikita
which question is zero
Faizan
sorry it is (5,16) in place of (n,b)
Faizan
I got. thanks. it is zero.
Faizan
a random variable having binomial distribution is?
Bokaho