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Statistics

Rosalia R. Arao, Ma.Teresa B. Arce, Antonio Roland I

Chapter 3

Types of Probability Distribution - all with Video Answers

Educators

Section 1

Exercise 8

07:17

Problem 1

Define the following:
a. Probability distribution
b. Binomial distribution
c. Poisson distribution
d. Normal distribution

Jerelyn Nevil
Jerelyn Nevil
Numerade Educator
02:50

Problem 2

Present 5 examples of binomial experiment other than those given in the discussion.

Wendi Zhao
Wendi Zhao
Numerade Educator
01:57

Problem 3

Present the different characteristics of binomial distribution, Poisson distribution, and normal distribution.

Sheryl Ezze
Sheryl Ezze
Numerade Educator
03:13

Problem 4

Construct a histogram of binomial probability distribution of tossing a coin 7 times.

Wendi Zhao
Wendi Zhao
Numerade Educator
00:32

Problem 5

Suppose that $x$ has a Poisson with a parameter $\mu=7.5$. Find:
a. $P(x=5)$
b. $P(x \geq 6)$
c. $P(x \geq 4)$
d. The mean of $x$
e. The standard deviation of $x$

Sriparna Bhattacharjee
Sriparna Bhattacharjee
Numerade Educator
05:02

Problem 6

Assume a binomial distribution where $n=25$ and $p=36 \%$
a. Find the probability that $x=20$.
b. Find the probability that $x \leq 5$
c. Find the probability that $x \geq 21$
d. Determine the mean, variance, and standard deviation of the distribution.

Robin Corrigan
Robin Corrigan
Numerade Educator
03:59

Problem 7

In a recent survey, $95 \%$ of the students in a certain university have cell phones. In a sample of 30 students, what is the probability?
a. that all 30 students have cell phones
b. that less than 4 students have cell phones
c. that more than 22 students have cell phones
d. that at least 20 students have cell phones

Lynn Larson
Lynn Larson
Numerade Educator
00:54

Problem 8

Find the probability of getting exactly four 3 's in tossing a die 6 times.

Weston Bell-Geddes
Weston Bell-Geddes
Numerade Educator
00:45

Problem 9

The probability that a patient in a certain provincial hospital recovers from a heart disease is $35 \%$. In a sample of 12 patients with heart disease, find the probability:
a. that at least 10 will survive
b. that 5 to 11 will survive
c. that exactly 10 will survive

Hast Aggarwal
Hast Aggarwal
Numerade Educator
05:46

Problem 10

Jay-R is a basketball player and his 3 -point shooting average is $85 \%$. What is the probability that he shoots exactly 4 in his 7 attempts?

Robin Corrigan
Robin Corrigan
Numerade Educator
04:21

Problem 11

The receptionist of JVMRG Hotel received an average of 5 phone calls every hour. What is the probability?
a. that on the next hour she will receive exactly 6 phone calls
b. that on the next hour she will receive at most 10 phone calls
c. that on the next hour she will receive from 7 to 9 phone calls
d. that on the next hour she will receive at least 8 phone calls

Prabhakar Kumar
Prabhakar Kumar
Numerade Educator
00:34

Problem 12

An encoder has an average of 3 encoding errors committed every page. What is the probability?
a. that the encoder will make at least 6 errors on the next page
b. that the encoder will make at most 4 errors on the next page
c. that the encoder will make exactly 7 errors on the next page

Hast Aggarwal
Hast Aggarwal
Numerade Educator
09:27

Problem 13

The number of students per hour entering the library has Poisson distribution. Library record shows that an average of 500 students enters the library during 1: 00 p.m. to 2: 00 p.m. Find the probability that at least 575 students enter the library during 1: 00 p.m. to 2: 00 p.m.

Evelyn Cunningham
Evelyn Cunningham
Numerade Educator
02:16

Problem 14

The average life of the RGC type of motor is 8 years, with a standard deviation of 1.5 years. If the manufacturer is willing to replace only $5 \%$ of the motors that fails, how long is the guarantee that he can offer? Assume that the lives of the motors follow a normal distribution.

Raymond Matshanda
Raymond Matshanda
Numerade Educator
06:19

Problem 15

Find the area under the normal curve of the following. Using the z-table, sketch the graph of each item below.
a. between $z=0$ and $z=2.25$
b. to the right of $z=2.64$
c. between $z=-1.75$ and $z=1.20$
d. to the left of $z=-2.15$
e. between $z=2.35$ and $z=2.95$

MA
Melissa A
Numerade Educator
06:33

Problem 16

According to the study, the mean salary of the workers is $\mathrm{P} 250$ per day with standard deviation of $\mathrm{P} 10 .$ Assuming that the distribution of salaries is normally distributed.
a. What is the probability that the workers received a salary between $\mathrm{P} 245$ and $\mathrm{P} 275$ per day?
b. What is the probability that the workers received a salary higher than or equal to $\mathrm{P} 285$ per day?
c. What is the probability that the workers received a salary of lower than or equal to $\mathrm{P} 240$ per day?
What is the probability that the workers received a salary between $\mathrm{P} 230$ and $\mathrm{P} 250$ per day?

Jon Southam
Jon Southam
Numerade Educator
01:55

Problem 17

Using problem number $16,$ assuming that there are 500 workers in a certain company.
a. How many of them received a salary between $\mathrm{P} 245$ and $\mathrm{P} 275$ per day?
b. How many of them received a salary higher than or equal to $\mathrm{P} 285$ per day?
c. How many of them received a salary lower than or equal to $\mathrm{P} 240$ per day?
d. How many of them received a salary between $\mathrm{P} 230$ and $\mathrm{P} 250$ per day?

Heather Zimmers
Heather Zimmers
Numerade Educator
11:04

Problem 18

From the past records of Ritz Glenn Restaurant, an average of 15 customers eats their snacks between 9: 30 a.m. to 10: 30 a.m. Assuming that the number of customers has eaten their snacks between 9: 30 a.m. to 10: 30 a.m., find the probability:
a. that exactly 10 customers have eaten their snacks
b. that at least 12 customers have eaten their snacks
c. that at most 8 customers have eaten their snacks

Robin Corrigan
Robin Corrigan
Numerade Educator
01:28

Problem 19

Prof. Luis Adrian Vinz constructed a multiple-choice test consisting of 10 questions. Each question has 4 choices with only one correct answer. Find the probability:
a. that the students get all correct answers
b. that the students get at least 8 correct answers
c. that the students get at most 5 correct answers
d. that the students get exactly 7 correct answers

Manisha Sarker
Manisha Sarker
Numerade Educator
00:14

Problem 20

RL Company manufactured light bulbs. The record showed that the mean lifetime of the light bulbs is 600 hours with a standard deviation of 210 hours. Assuming that the lifetime of light bulbs is normally distributed. Find the probability that:
a. a light bulb will have a lifetime between 620 hours and 660 hours
b. a light bulb will have a lifetime exceeding 648 hours
c. a light bulb will have a lifetime of at most 480 hours

M Hassan Anwar
M Hassan Anwar
Numerade Educator