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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

3 years ago

How many faces does a square pyramid have? three four five six

andrew-mc [135]

Answer:

5

Step-by-step explanation:

3 0

3 years ago

Read 2 more answers

Answer 3,4,5 to get 15 points.

masha68 [24]

Answer:True, true, true.

Step-by-step explanation:

8 0

3 years ago

Read 2 more answers

3,4,4,5,5,6,6,6,6,7,9,12,14,15 Min: Q1: Med: Q3: Max:

kolezko [41]

Answer:

Median ( Q2) = 6

Q1 ( lower quartile) = 4.5

Q3 ( upper quaartile) = 10.5

Step-by-step explanation:

3,4,4,5,5,6, 6,6 ,6,7,9,12,14,15

6,6 is the median but we only need I median. So 6 + 6 = 12, 12 divided 2 = 6.

3,4,4,5,5,6, is the Q1 ( lower quartile ) and median of Q1, is 4,5. 4 + 5 = 9. 9 divided 2 = 4.5

6,7,9,12,14,15 is Q3 ( upper quartile) 9,12 is median but we only need one. So 9 + 12 =21. 21 divided 2 = 10.5

5 0

3 years ago

If x2 + y2 = 38 and x - y = 2, then what is x? If there are two possible answers, then enter the larger of the two.

Ket [755]

If x-y=2 then x=2+y

And if you insert that in the first equation

$(2 + y) {}^{2} + y {}^{2} = 38$
$4 + 4y + y {}^{2} + {y}^{2} = 38$
$2y {}^{2} + 4y - 34 = 0$
$y = - 1 + \sqrt{17}$
Or
$y = - 1 - \sqrt{17}$

The first one is bigger so the answer is

$y = - 1 - \sqrt{17}$

7 0

3 years ago

Read 2 more answers