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. Answer the following questions. Question 2 (4 points). Find the probability that this box will contain at most 20 defective light bulbs. Show your work or calculator input. (Round your answer to 4 places after the decimal point). Question 3 (2 points): How many defective light bulbs are expected to be found in such boxes, on average? Show your work Question 4 (3 points): Find the standard deviation of defective light bulbs in this case. Show your work. (Round your answer to 2 places after the decimal point).

(a) P(X 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.;

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, = = = 15

Standard deviation of X, = = = 3.7

So, X ~ N(

Now, the z score probability distribution is given by;

                Z = ~ N(0,1)

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

    P(X < 20.5) = P( < ) = P(Z < 1.49) = 0.9319

(b) Expected number of defective light bulbs found in such boxes, on average is given by = E(X) = = = 15.

Standard deviation of defective light bulbs is given by = S.D. = = = 3.67

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step-by-step explanation:

plants store their excess carbohydrate in the form of starch so that it could be used as energy source later on. the excess carbohydrate is converted into starch in the plastid i.e. chloroplast & this process occurs in the presence of sunlight. it is an insoluble polymer of glucose which gets stored in cell organelles named as amyloplasts. in some plants, starch is also stored in roots and embryos.