Ask question

Ask question

All categories

2 years ago

6

Among 35 students in a class, 20 of them earned A's on the midterm exam, 13 earned A's on the nal exam, and 12 did not earn A's

on either examination. What is the probability that a random

1 answer:

enyata [817]2 years ago

7 0

Answer:

The correct answer is " $\frac{2}{7}$ ".

Step-by-step explanation:

According to the question,

Number of students,

= 35

A ! mid term A,

$n(A) = 20$

B : final A,

$n(B) = 13$

Didn't start,

$n(A^c \cap B^c) = 12$

Now,

⇒ $n(A \cup B)=35-12$

$=23$

then,

⇒ $n(A \cup B)=20+13-23$

$=10$

hence,

The probability will be:

⇒ $P(A \cap B)=\frac{10}{35}$

⇒ $=\frac{2}{7}$

You might be interested in

Please help with this

mr Goodwill [35]

Answer: x = 1.50551927,2.68790604

Step-by-step explanation:

8 0

3 years ago

Alien probe is stretched between the top and a stake in the ground the head of the state is at ground level the rope also touche

Aleksandr-060686 [28]

The building is about 20 to 21 feet tall.

6 0

2 years ago

During the 2005 football season, Team Tackle beat Team Sack by 6 points. If their combined scores totaled 60, find the individ

Travka [436]

2x+6=60

2x=60-6

2x=54

x=54/2

x=27

27+27+6=60

8 0

2 years ago

Create a list of steps, in order, that will solve the following equation.

AleksandrR [38]

Step-by-step explanation:

Add 1 to both sides

Multiply both sides by 4

Take the square root of both sides

Subtract 5 from both sides

(straight from khan academy hints)

8 0

3 years ago

Let X1, X2, ... , Xn be a random sample from N(μ, σ2), where the mean θ = μ is such that −[infinity] < θ < [infinity] and

Sliva [168]

Answer:

$l'(\theta) = \frac{1}{\sigma^2} \sum_{i=1}^n (X_i -\theta)$

And then the maximum occurs when $l'(\theta) = 0$ , and that is only satisfied if and only if:

$\hat \theta = \bar X$

Step-by-step explanation:

For this case we have a random sample $X_1 ,X_2,...,X_n$ where $X_i \sim N(\mu=\theta, \sigma)$ where $\sigma$ is fixed. And we want to show that the maximum likehood estimator for $\theta = \bar X$ .

The first step is obtain the probability distribution function for the random variable X. For this case each $X_i , i=1,...n$ have the following density function:

$f(x_i | \theta,\sigma^2) = \frac{1}{\sqrt{2\pi}\sigma} exp^{-\frac{(x-\theta)^2}{2\sigma^2}} , -\infty \leq x \leq \infty$

The likehood function is given by:

$L(\theta) = \prod_{i=1}^n f(x_i)$

Assuming independence between the random sample, and replacing the density function we have this:

$L(\theta) = (\frac{1}{\sqrt{2\pi \sigma^2}})^n exp (-\frac{1}{2\sigma^2} \sum_{i=1}^n (X_i-\theta)^2)$

Taking the natural log on btoh sides we got:

$l(\theta) = -\frac{n}{2} ln(\sqrt{2\pi\sigma^2}) - \frac{1}{2\sigma^2} \sum_{i=1}^n (X_i -\theta)^2$

Now if we take the derivate respect $\theta$ we will see this:

$l'(\theta) = \frac{1}{\sigma^2} \sum_{i=1}^n (X_i -\theta)$

And then the maximum occurs when $l'(\theta) = 0$ , and that is only satisfied if and only if:

$\hat \theta = \bar X$

6 0

3 years ago