Ikunupe6v

2021-12-18

a) Market research has shown that 60% of persons who are introduced to a certain product actually buy the product. A random sample of 15 persons were introduced to the product.

i. Define the variable of interest for this scenario.

ii. What probability distribution do you think best describes the situation? Why?

iii. Calculate the probability that exactly 9 will buy the product.

i. Define the variable of interest for this scenario.

ii. What probability distribution do you think best describes the situation? Why?

iii. Calculate the probability that exactly 9 will buy the product.

eskalopit

Beginner2021-12-19Added 31 answers

Step 1

a) The proportion of persons actually buying the introduced product can be considered as success and proportion of persons not buying the product can be considered as failure.

i. Let X be a variable defined as the number of persons actually buying the introduced product. This is the variable of interest.

ii. The probability distribution suitable for describing this situation is the Binomial Distribution. This is because we are looking for the number of success (number of persons buying the product).

iii. The probability mass function for Binomial distribution is given by:

$P(X=x){=}^{n}{C}_{x}\cdot {p}^{x}.{(1-p)}^{n-x}$ , where n is the total number of items (in this case persons) and x is the number of success (in this case, persons buying the product).

Step 2

The probability of success is:$p=0.60$ .

The sample size is:$n=15$

$P(X=9){=}^{15}{C}_{9}.{\left(0.60\right)}^{9}.{\left(0.40\right)}^{15-9}$

$=\frac{15!}{9!.6!}.\left(0.010078\right)\left(0.004096\right)$

$=0.2066$

a) The proportion of persons actually buying the introduced product can be considered as success and proportion of persons not buying the product can be considered as failure.

i. Let X be a variable defined as the number of persons actually buying the introduced product. This is the variable of interest.

ii. The probability distribution suitable for describing this situation is the Binomial Distribution. This is because we are looking for the number of success (number of persons buying the product).

iii. The probability mass function for Binomial distribution is given by:

Step 2

The probability of success is:

The sample size is:

Annie Gonzalez

Beginner2021-12-20Added 41 answers

Step 1

Solution:

1. a.

Here, it is needed to identify the proportion of persons who are introduced to a certain product actually buy the product.

Thus, the variable of interest is the proportion of person who is introduced to a certain product actually buys the product.

Step 2

1. Let X be the number of persons buy the product and n be the sample number of persons were introduced to the product.

From the given information, probability of person who is introduced to a certain product actually buys the product is 0.60 and$n=15$ .

Here, persons are independent and probability of success is constant. Hence, X follows binomial distribution with parameters$n=15\text{}{\textstyle \phantom{\rule{1em}{0ex}}}\text{and}{\textstyle \phantom{\rule{1em}{0ex}}}\text{}p=0.60$ .

Thus, the probability distribution describes the distribution is Binomial.

Step 3

iii. The probability mass function of binomial random variable X is

$$P(X=x)=(\begin{array}{c}n\\ x\end{array}){p}^{x}(1-p{)}^{n-x};x=0,1,...,n$$

The probability that exactly 9 will buy the product is

$$P(X=9)=(\begin{array}{c}15\\ 9\end{array}){0.60}^{9}(1-0.60{)}^{15-9}$$

$=0.2066$

Thus, the probability that exactly 9 will buy the product is 0.2066.

Step 4

1. The number of persons who are expected to buy the product if 80 persons are introduced to the product is

$E\left(X\right)=np$

$=80\left(0.60\right)$

$=48$

Thus, the number of persons who are expected to buy the product if 80 persons are introduced to the product is 48.

Solution:

1. a.

Here, it is needed to identify the proportion of persons who are introduced to a certain product actually buy the product.

Thus, the variable of interest is the proportion of person who is introduced to a certain product actually buys the product.

Step 2

1. Let X be the number of persons buy the product and n be the sample number of persons were introduced to the product.

From the given information, probability of person who is introduced to a certain product actually buys the product is 0.60 and

Here, persons are independent and probability of success is constant. Hence, X follows binomial distribution with parameters

Thus, the probability distribution describes the distribution is Binomial.

Step 3

iii. The probability mass function of binomial random variable X is

The probability that exactly 9 will buy the product is

Thus, the probability that exactly 9 will buy the product is 0.2066.

Step 4

1. The number of persons who are expected to buy the product if 80 persons are introduced to the product is

Thus, the number of persons who are expected to buy the product if 80 persons are introduced to the product is 48.

nick1337

Expert2021-12-28Added 777 answers

Step 1

NSK

1. A random variable X, is said to follow binomial distribution if the probability mass function of X is,

Here, n is total number of trials and p is the success probability.

The random variable X, that defines the number of persons, who are introduced to a certain product actually buy the product.

Step 3

ii. Here, n= the total number of all persons, who are introduced to the product. There are total 15 persons, who are introduced to the product.

It is obtained that, 60% of persons who are introduced to a certain product actually buy the product. Thus, the success probability is p = 0.6.

In this case, there are two outcomes, such that, whether the person buy the product or not. These two events are independent to each other, and the probabilities of success are independent for each trial.

Thus, X follows Binomial distribution with number of trials 15 and success probability 0.6.

Thus, the binomial probability distribution describe the situation most.

Step 4

iii. The probability that exactly 9 will buy the product is,

Thus, the probability that exactly 9 will buy the product is 0.2066.

Assume that when adults with smartphones are randomly selected, 54% use them in meetings or classes (based on data from an LG Smartphone survey). If 8 adult smartphone users are randomly selected, find the probability that exactly 6 of them use their smartphones in meetings or classes?

Write formula for the sequence of -4, 0, 8, 20, 36, 56, 80, where the order of f(x) is 0, 1, 2, 3, 4, 5, 6 respectively

A binomial probability experiment is conducted with the given parameters. Compute the probability of x successes in the n independent trials of the experiment.n=20,

p=0.7,

x=19

P(19)=

In binomial probability distribution, the dependents of standard deviations must includes.

a) all of above.

b) probability of q.

c) probability of p.

d) trials.The probability that a man will be alive in 25 years is 3/5, and the probability that his wifewill be alive in 25 years is 2/3

Determine the probability that both will be aliveHow many different ways can you make change for a quarter??

(Different arrangements of the same coins are not counted separately.)One hundred people line up to board an airplane that can accommodate 100 passengers. Each has a boarding pass with assigned seat. However, the first passenger to board has misplaced his boarding pass and is assigned a seat at random. After that, each person takes the assigned seat. What is the probability that the last person to board gets his assigned seat unoccupied?

A) 1

B) 0.33

C) 0.6

D) 0.5The value of $(243{)}^{-\frac{2}{5}}$ is _______.

A)9

B)$\frac{1}{9}$

C)$\frac{1}{3}$

D)01 octopus has 8 legs. How many legs does 3 octopuses have?

A) 16

B 24

C) 32

D) 14From a pack of 52 cards, two cards are drawn in succession one by one without replacement. The probability that both are aces is...

A pack of cards contains $4$ aces, $4$ kings, $4$ queens and $4$ jacks. Two cards are drawn at random. The probability that at least one of these is an ace is A$\frac{9}{20}$ B$\frac{3}{16}$ C$\frac{1}{6}$ D$\frac{1}{9}$

You spin a spinner that has 8 equal-sized sections numbered 1 to 8. Find the theoretical probability of landing on the given section(s) of the spinner. (i) section 1 (ii) odd-numbered section (iii) a section whose number is a power of 2. [4 MARKS]

If A and B are two independent events such that $P(A)>0.5,P(B)>0.5,P(A\cap \overline{B})=\frac{3}{25}P(\overline{A}\cap B)=\frac{8}{25}$, then the value of $P(A\cap B)$ is

A) $\frac{12}{25}$

B) $\frac{14}{25}$

C) $\frac{18}{25}$

D) $\frac{24}{25}$The unit of plane angle is radian, hence its dimensions are

A) $[{M}^{0}{L}^{0}{T}^{0}]$

B) $[{M}^{1}{L}^{-1}{T}^{0}]$

C) $[{M}^{0}{L}^{1}{T}^{-1}]$

D) $[{M}^{1}{L}^{0}{T}^{-1}]$Clinical trial tests a method designed to increase the probability of conceiving a girl. In the study, 340 babies were born, and 289 of them were girls. Use the sample data to construct a 99% confidence interval estimate of the percentage of girls born?