Q1. Using Binomial distribution to calculate the probability of getting less tha

Question

Q1. Using Binomial distribution to calculate the probability of getting less than 3 times of “5” in 8 time throws of a fair die?Q2. Using random number to generate 2000 numbers (from -1 to 1) and find mean, standard deviation, variance of these 2000 numbers, and plot histogramof these 2000 numbers.Q3. A quality control unit inspects 400 pieces products every day. If 3% of the products have defects, what is the highest number of defective products will be found? And what is the probability? python or matlab

Explanation / Answer

1.

You want to find the probability of rolling no more than 3 fives. "no more than 3" can be rephrases as "3 or fewer" or "less than or equal to 3". The possible results you want are:

0 fives

1 five

2 fives

This is a binomial distribution problem, since the two possible results are {5, not 5}, the probability of rolling a 5 doesn't change between rolls, and there's a fixed number of trials (8 rolls.)

With a probability of a single rolls success p, and failure q, the formula for finding the probability of x successes out of n rolls is:

P(x) = nCx px qn-x

The probability p of rolling a 5 in a single roll is 1/6.

The probability q of not rolling a 5 is 5/6.

n = 8.

You then need to calculate

P(x<3) = P(x=0) + P(x=1) + P(x=2)

P(x=0) = 8C0 (1/6)0 (5/6)8

P(x=1) = 8C1 (1/6)1 (5/6)7

P(x=2) = 8C2 (1/6)2 (5/6)6

and then add them all up

Related Questions

Navigate

• Browse (All)
• Browse Q
• Subjects

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.