Find the sum of (6d+5)-(2-3d)

For each student, there are only two possible outcomes. Either they have a laptop, or they do not. The probability of a student having a laptop is independent from other students. So we use the binomial probability distribution to solve this question.

Binomial probability distribution

The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.

$P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}$

In which $C_{n,x}$ is the number of different combinations of x objects from a set of n elements, given by the following formula.

$C_{n,x} = \frac{n!}{x!(n-x)!}$

And p is the probability of X happening.

A study indicates that 62% of students have have a laptop.

This means that $n = 0.62$

You randomly sample 8 students.

This means that $n = 8$

Find the probability that between 4 and 6 (including endpoints) have a laptop.

$P(4 \leq X \leq 6) = P(X = 4) + P(X = 5) + P(X = 6)$

$P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}$

$P(X = 4) = C_{8,4}.(0.62)^{4}.(0.38)^{4} = 0.2157$

$P(X = 5) = C_{8,5}.(0.62)^{5}.(0.38)^{3} = 0.2815$

$P(X = 6) = C_{8,6}.(0.62)^{6}.(0.38)^{2} = 0.2297$

$P(4 \leq X \leq 6) = P(X = 4) + P(X = 5) + P(X = 6) = 0.2157 + 0.2815 + 0.2297 = 0.7269$

72.69% probability that between 4 and 6 (including endpoints) have a laptop.

3 0

3 years ago

Can someone explain this differentiation question to me? I can differentiate but then I'm not sure what I am doing

weeeeeb [17]

note that gradient = $\frac{dy}{dx}$ at x = a

calculate $\frac{dy}{dx}$ for each pair of functions and compare gradient

(a)

$\frac{dy}{dx}$ = 2x and $\frac{dy}{dx}$ = - 1

at x = 4 : gradient = 8 and - 1 : 8 > - 1

(b)

$\frac{dy}{dx}$ = 2x + 3 and $\frac{dy}{dx}$ = - 2

at x = 2 : gradient = 7 and - 2 and 7 > - 2

(c)

$\frac{dy}{dx}$ = 4x + 13 and $\frac{dy}{dx}$ = 2

at x = - 7 : gradient = - 15 and 2 and 2 > - 15

(d)

$\frac{dy}{dx}$ = 6x - 5 and $\frac{dy}{dx}$ = 2x - 2

at x = - 1 : gradient = - 11 and - 4 and - 4 > - 11

(e)

y = √x = $x^{\frac{1}{2} }$

$\frac{dy}{dx}$ = 1/(2√x) and $\frac{dy}{dx}$ = 2

at x = 9 : gradient = $\frac{1}{6}$ and 2 and 2 > $\frac{1}{6}$

4 0

3 years ago

A store asked 250 of its customers whether or not they were satisfied with the service. The responses were also classified accor

anyanavicka [17]

Answer:

Correct option: e) a two-way table.

Step-by-step explanation:

In this case the store wants to see whether there is a relationship between the satisfaction level of the customer and their gender.

In statistics when there is a need to analyze or derive a relation between two categorical variables one should use a two-way table.

Categorical variables are qualitative variables that take on specific values that are usually labels. For example, grades obtained in an exam, gender, etc.

In this case the two categorical variables are: Gender and Satisfaction level.

To study the relation between the gender of a customer and their satisfaction level use a two-way table.

3 0

2 years ago