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3 years ago

Suppose the discrete random variable X has the probability distribution below:

Mathematics

1 answer:

Talja [164]3 years ago

4 0

(a) P(X < 3) = P(X = 0) + P(X = 1) + P(X = 2) = 0.11 + 0.52 + 0.19 = 0.82

(b) P(X ≥ 1) = P(X = 1) + P(X = 2) + P(X = 3) + P(X = 4) = 0.52 + 0.19 + 0.12 + 0.06 = 0.89

(d) σ² = (0²×0.11 + 1²×0.52 + 2²×0.19 + 3²×0.12 + 4²×0.06) - µ² = 1.07

σ = √(σ²) ≈ 1.03

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A high school mathematics teacher can grade a set of exams in 7 hours working alone. If their student teacher helps them, it wi

Stels [109]

It takes 9 hrs 19.8 minutes for the student teacher to grade the exams if they worked alone

<u>Solution:</u>

Let the efficiency of the school teacher be “x” and the efficiency of the student teacher be “y”

Here the word efficiency means the rate of doing work

Let the total work to be completed be W

According to the question,

The time taken by the school teacher to complete the work is 7 hrs.

So we can write it in equation form

$W = x \times 7$ ---- eqn 1

where W is the total work and x is the efficiency

Similarly for student teacher and school teacher doing the work simultaneously, we can write the equation as

$W =(x +y ) \times 4$

Equating eqn 1 and 2

$x \times 7=(x+y) \times 4$

7x = 4x + 4y

3x = 4y

So in ratio x : y = 4 : 3

Now putting value of x = 4 in equation (1) we get total work to be 28

Now, <em>total time taken by the student teacher = total work ÷ efficiency of student teacher</em>

Hence, total time taken by the student teacher = 28 ÷ 3 = 9.33 hrs

= 9 hrs 19.8 minutes

Hence it takes 9 hrs 19.8 minutes for the student teacher to grade the exams if they worked alone

4 0

3 years ago

Three fourths of the fruit in a refrigerator

VashaNatasha [74]

Answer:32 fruits

Step-by-step explanation:

3/4=24/?

24÷3=8

8×4=32

4 0

3 years ago

Find the product of 2(5.9) mentally using the distributive property.

VARVARA [1.3K]

2(5.9) is 11.8

Hopefully i is right I did this in my head.

7 0

2 years ago

Find the zeros of the function. Enter the solutions from least to greatest.

Harman [31]

9514 1404 393

Answer:

x = 5, x = 11

Step-by-step explanation:

Set f(x) = 0 and solve for x.

0 = (x -8)² -9

9 = (x -8)² . . . . . add 9

±√9 = x -8 . . . . . take the square root

±3 +8 = x . . . . . . . add 8

That is, ...

x = 8 -3 = 5 . . . . lesser x

x = 8 +3 = 11 . . . greater x

3 0

2 years ago

Cubed root x cubed root x2

Yuki888 [10]

Answer:

Final answer is $\sqrt[3]{x^1}\cdot\sqrt[3]{x^2}=x$ .

Step-by-step explanation:

Given problem is $\sqrt[3]{x}\cdot\sqrt[3]{x^2}$ .

Now we need to simplify this problem.

$\sqrt[3]{x}\cdot\sqrt[3]{x^2}$

$\sqrt[3]{x^1}\cdot\sqrt[3]{x^2}$

Apply formula

$\sqrt[n]{x^p}\cdot\sqrt[n]{x^q}=\sqrt[n]{x^{p+q}}$

so we get:

$\sqrt[3]{x^1}\cdot\sqrt[3]{x^2}=\sqrt[3]{x^{1+2}}$

$\sqrt[3]{x^1}\cdot\sqrt[3]{x^2}=\sqrt[3]{x^{3}}$

$\sqrt[3]{x^1}\cdot\sqrt[3]{x^2}=x$

Hence final answer is $\sqrt[3]{x^1}\cdot\sqrt[3]{x^2}=x$ .

7 0

3 years ago