Please please i need help i did not understand it please do it .........

A contractor is required by a county planning department to submit one, two, three, four, or five forms (depending on the nature

Westkost [7]

Answer:

(a) The value of k is $\frac{1}{15}$ .

(b) The probability that at most three forms are required is 0.40.

(c) The probability that between two and four forms (inclusive) are required is 0.60.

(d) $P(y)=\frac{y^{2}}{50} ;\ y=1, 2, ...5$ is not the pmf of y.

Step-by-step explanation:

The random variable Y is defined as the number of forms required of the next applicant.

The probability mass function is defined as:

$P(y) = \left \{ {{ky};\ for \ y=1,2,...5 \atop {0};\ otherwise} \right$

(a)

The sum of all probabilities of an event is 1.

Use this law to compute the value of k.

$\sum P(y) = 1\\k+2k+3k+4k+5k=1\\15k=1\\k=\frac{1}{15}$

Thus, the value of k is $\frac{1}{15}$ .

(b)

Compute the value of P (Y ≤ 3) as follows:

$P(Y\leq 3)=P(Y=1)+P(Y=2)+P(Y=3)\\=\frac{1}{15}+\frac{2}{15}+ \frac{3}{15}\\=\frac{1+2+3}{15}\\ =\frac{6}{15} \\=0.40$

Thus, the probability that at most three forms are required is 0.40.

(c)

Compute the value of P (2 ≤ Y ≤ 4) as follows:

$P(2\leq Y\leq 4)=P(Y=2)+P(Y=3)+P(Y=4)\\=\frac{2}{15}+\frac{3}{15}+\frac{4}{15}\\ =\frac{2+3+4}{15}\\ =\frac{9}{15} \\=0.60$

Thus, the probability that between two and four forms (inclusive) are required is 0.60.

(d)

Now, for $P(y)=\frac{y^{2}}{50} ;\ y=1, 2, ...5$ to be the pmf of Y it has to satisfy the conditions:

$P(y)=\frac{y^{2}}{50}>0;\ for\ all\ values\ of\ y \\$
$\sum P(y)=1$

Check condition 1:

$y=1:\ P(y)=\frac{y^{2}}{50}=\frac{1}{50}=0.02>0\\y=2:\ P(y)=\frac{y^{2}}{50}=\frac{4}{50}=0.08>0 \\y=3:\ P(y)=\frac{y^{2}}{50}=\frac{9}{50}=0.18>0\\y=4:\ P(y)=\frac{y^{2}}{50}=\frac{16}{50}=0.32>0 \\y=5:\ P(y)=\frac{y^{2}}{50}=\frac{25}{50}=0.50>0$

Condition 1 is fulfilled.

Check condition 2:

$\sum P(y)=0.02+0.08+0.18+0.32+0.50=1.1>1$

Condition 2 is not satisfied.

Thus, $P(y)=\frac{y^{2}}{50} ;\ y=1, 2, ...5$ is not the pmf of y.

7 0

2 years ago

The following information is known about a loan.

Katyanochek1 [597]

Use the formula I = PRT.....you'll get $2000

6 0

2 years ago

Read 2 more answers

Derek's score on a test was 90 percent. He had 72 questions right. How many problems were on the test?

romanna [79]

90% = 72 questions

\\Find 1%

1 % = 72 ÷ 90 = 0.8

\\Find 100%

100% = 0.8 x 100 = 80 questions

Answer: There were 80 questions

6 0

3 years ago

Find the value of x that makes m ∥ n .

Alla [95]

Answer:

60

Step-by-step explanation:

(2x+15)=135 They're corresponding angles so they equal/congruent

-15 -15 Subtract 15 on both sides since you're looking for x

2x = 120 Bring down the remains and subtract 135 from 15

2 2 Add 2 on both sides

x= 60 Divide.

3 0

2 years ago

write the standard form point slope form and slope intercept form of a line that passes through (-7,6) and has a slope of. -1

TEA [102]

Answer: See explanation

Step-by-step explanation:

Point slope form: y - y₁ = m (x - x₁)

y₁ = 6

x₁ = -7

y - 6 = -1 (x - [-7])

y - 6 = -1 (x + 7)

y - 6 = -1x - 7

Add 6 to both sides

y = -1x - 1 or y = -x -1

Slope intercept form: y = mx + b

m = -1

b = 6

y = -1x + 6 or y = -x + 6

Standard form: Ax + By = C

Change slope intercept form into _x + _y = c

Slope intercept form: y = -x + 6

Standard form:

y = -x + 6

Add x to both sides

x + y = 6 or -x - y = -6

Hope I helped!

5 0

2 years ago