If Brenda drank 24 pints of milk how much did Jasmine drink

A manufacturer of Christmas light bulbs knows that 10% of these bulbs are defective. It is known that light bulbs are defective

Inessa05 [86]

Answer:

(a) P(X $\leq$ 20) = 0.9319

(b) Expected number of defective light bulbs = 15

Step-by-step explanation:

We are given that a manufacturer of Christmas light bulbs knows that 10% of these bulbs are defective. It is known that light bulbs are defective independently. A box of 150 bulbs is selected at random.

Firstly, the above situation can be represented through binomial distribution, i.e.;

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

where, n = number of samples taken = 150

r = number of success

p = probability of success which in our question is % of bulbs that

are defective, i.e. 10%

Now, we can't calculate the required probability using binomial distribution because here n is very large(n > 30), so we will convert this distribution into normal distribution using continuity correction.

So, Let X = No. of defective bulbs in a box

Mean of X, $\mu$ = $n \times p$ = $150 \times 0.10$ = 15

Standard deviation of X, $\sigma$ = $\sqrt{np(1-p)}$ = $\sqrt{150 \times 0.10 \times (1-0.10)}$ = 3.7

So, X ~ N( $\mu = 15, \sigma^{2} = 3.7^{2})$

Now, the z score probability distribution is given by;

Z = $\frac{X-\mu}{\sigma}$ ~ N(0,1)

(a) Probability that this box will contain at most 20 defective light bulbs is given by = P(X $\leq$ 20) = P(X < 20.5) ---- using continuity correction

P(X < 20.5) = P( $\frac{X-\mu}{\sigma}$ < $\frac{20.5-15}{3.7}$ ) = P(Z < 1.49) = 0.9319

(b) Expected number of defective light bulbs found in such boxes, on average is given by = E(X) = $n \times p$ = $150 \times 0.10$ = 15.

5 0

3 years ago

What is the solution to -5m = -40? m = -8 m = 200 m = -200 m = 8

Murljashka [212]

Answer:

The answer would be M = positive 8

Step-by-step explanation:

-5 times 8 = -40

7 0

2 years ago

Read 2 more answers

What is (-2, -1) rotated 90 degrees clock wise

Savatey [412]

Answer:

(-1, 2)

Step-by-step explanation:

If we have a point (h,k) and it is rotated 90 degrees clockwise, the resulting point will have coordinates (k, -h).

So, basically the y coordinate becomes the x coordinate and x coordinate becomes the NEGATIVE of the y coordinate.

The point to rotate is (-2, -1), so after 90 degree clockwise rotation, it will become:

(-1, -(-2))

= (-1, 2)

This is the answer.

4 0

3 years ago

Highlight very briefly why/how when you subtract a negative number, that it yields a positive number. Will give brainliest

lbvjy [14]

When we build integers from natural numbers, we're looking for additive inverse of natural numbers?

What's an additive inverse? Well, for example, the additive inverse of 2 is a numbers $x$ such that

$2+x = 0$

We call this number -2. So, the real meaning behind the negative sign is "if you add me and my positive counterpart, the result is zero".

So, -5 is the additive inverse of 5, -16 is the additive inverse of 16, and so on, because

$5-5=0,\quad 16-16=0,\ldots$

Note that this is a symmetrical relation: if -5 is the inverse of 5, it is also true that 5 is the inverse of -5.

So, when you write something like

$5-(-4)$

it means that you want to add 5 and the inverse of the inverse of 4. But given what we just said, the inverse of the inverse of a number is the number itself, which is why subtracting a negative number is the same as adding it.

3 0

2 years ago

A 10-foot ladder leans against a wall. It hits the wall 9 feet up. How far is the base of the ladder from the wall? Apply the Py

ElenaW [278]

A 10-foot ladder leans against a wall. It hits the wall 9 feet up. How far is the base of the ladder from the wall? Apply the Pythagorean Theorem to this problem

triangle

side S1 = 9 feet

hypotenuse H = 10 feet

side S2 - X = ?

the Pythagorean Theorem

H x H = S1 x S1 + S2 x S2 = S1 x S1 + X x X

X x X = H x H - S1 x S1 = 10 x 10 - 9 x 9 = 100 - 91 = 9

X x X = 9

X = 3

How far is the base of the ladder from the wall? 3 feet

check:

H x H = S1 x S1 + X x X

10 x 10 = 9 x 9 + 3 x 3

100 = 91 +9 = 100

7 0

3 years ago

If Brenda drank 24 pints of milk how much did Jasmine drink​

If Brenda drank 24 pints of milk how much did Jasmine drink