I need help with this

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

andriy [413]

Answer:

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

(b) Expected number of defective light bulbs = 15

(c) Standard deviation of defective light bulbs = 3.67

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.

Standard deviation of defective light bulbs is given by = S.D. = $\sqrt{np(1-p)}$ = $\sqrt{150 \times 0.10 \times (1-0.10)}$ = 3.67

8 0

2 years ago

Evaluate the expression when a= 4 and b= -7. -9a+b

Helen [10]

Answer:

-43

Step-by-step explanation:

So first things first you will multiply -9 by 4 and that gives you -36, Next you will add -7 to -36 which gives you -43.

$-9(4)+(-7)\\-36+(-7) \\= -43$

Hope this helps :D

4 0

2 years ago

Read 2 more answers

Can someone help mme

Vanyuwa [196]

Answer:

ok this is that and that is this.hope this helps

5 0

1 year ago

John read the first 114 pages of the novel, which was 3 less than 1/3 of the novel

Nastasia [14]

Let p = total pages in the book
114 pages of a novel which was 3 pages less than 1/3 
114 was 1/3 total pages - 3 pages 
114 = 1/3p - 3

6 0

2 years ago

Read 2 more answers

Angelica earns d dollars for babysitting each week. She also receives an allowance of $10 per week. The expression (10+d)∙5 can

Katyanochek1 [597]

Answer:

The amount of money Angelica will have at the end of five weeks if d = $25 is $175.

Step-by-step explanation:

The given information are;

The allowance Angelica earns for baby sitting = d dollars per week

The amount she receives as allowance = $10 per week

The amount she will have at the end of 5 weeks = (10 + d)·5

The amount, A, of money Angelica will have at the end of five weeks if d = $25 is given as follows;

A = (10 + 25) × 5 = $175

The amount of money Angelica will have at the end of five weeks if d = $25 is $175.

7 0

2 years ago