What is the next item in the sequence below? -324, 108, -36, 12,...

A company that produces fine crystal knows from experience that 13% of its goblets have cosmetic flaws and must be classified as

Kisachek [45]

Answer:

(a) The probability that only one goblet is a second among six randomly selected goblets is 0.3888.

(b) The probability that at least two goblet is a second among six randomly selected goblets is 0.1776.

(c) The probability that at most five must be selected to find four that are not seconds is 0.9453.

Step-by-step explanation:

Let X = number of seconds in the batch.

The probability of the random variable X is, p = 0.31.

The random variable X follows a Binomial distribution with parameters n and p.

The probability mass function of X is:

$P(X=x)={n\choose x}p^{x}(1-p)^{n-x};\ x=0,1,2,3...$

(a)

Compute the probability that only one goblet is a second among six randomly selected goblets as follows:

$P(X=1)={6\choose 1}0.13^{1}(1-0.13)^{6-1}\\=6\times 0.13\times 0.4984\\=0.3888$

Thus, the probability that only one goblet is a second among six randomly selected goblets is 0.3888.

(b)

Compute the probability that at least two goblet is a second among six randomly selected goblets as follows:

P (X ≥ 2) = 1 - P (X < 2)

$=1-{6\choose 0}0.13^{0}(1-0.13)^{6-0}-{6\choose 1}0.13^{1}(1-0.13)^{6-1}\\=1-0.4336+0.3888\\=0.1776$

Thus, the probability that at least two goblet is a second among six randomly selected goblets is 0.1776.

(c)

If goblets are examined one by one then to find four that are not seconds we need to select either 4 goblets that are not seconds or 5 goblets including only 1 second.

P (4 not seconds) = P (X = 0; n = 4) + P (X = 1; n = 5)

$={4\choose 0}0.13^{0}(1-0.13)^{4-0}+{5\choose 1}0.13^{1}(1-0.13)^{5-1}\\=0.5729+0.3724\\=0.9453$

Thus, the probability that at most five must be selected to find four that are not seconds is 0.9453.

8 0

3 years ago

Square with sides measuring 12in

malfutka [58]

Perimeter = 48in Area =144 in

4 0

3 years ago

What is the scale factor?

Fed [463]

Answer:

2

Step-by-step explanation:

it literally doubles in size

5 0

3 years ago

Read 2 more answers

Oint C is on line segment BD‾\overline{BD} BD . Given BD=5x,BD=5x, BD=5x, BC=4x,BC=4x, BC=4x, and CD=4,CD=4, CD=4, determine the

Gennadij [26K]

Answer:

Therefore the required value of $\overline{BD}$ is 20 units.

Step-by-step explanation:

Line Segment: Line segment is a portion of a line whose has two end points.

Given that point C is on the line segment $\overline{BD}$ .

$\overline{BD}$ = 5x , $\overline{BC}$ = 4x and $\overline{CD}$ = 4

C is the point of the line segment of $\overline{BD}$ .

So we can write

$\overline {BD}= \overline{BC}+\overline{CD}$

Putting the values of $\overline{BD}$ , $\overline{BC}$ and $\overline{CD}$

5x=4x+ 4

⇒5x-4x= 4

⇒x=4

So we get the value of x.

To get the value of $\overline{BD}$ , we need to put the value of x in the value of $\overline{BD}$ .

Therefore,

$\overline{BD}$ = 5×4

=20

Therefore the required value of $\overline{BD}$ is 20 units.

3 0

3 years ago

A number, n, is multiplied by -7/8. The product is -0.5. What is the value of n?

Yuki888 [10]

Answer: A.n = 4/7

have:

$n.\frac{-7}{8} =-0.5\\\\n.\frac{-7}{8}=\frac{-1}{2}\\\\n=\frac{-1}{2}:\frac{-7}{8}=\frac{4}{7}$

Step-by-step explanation:

3 0

3 years ago