SPDF VERSION 2 SM025

Multiple Choice

Why do you think understanding special probability distributions is important in mathematics and real-world applications?

• They help in predicting outcomes in uncertain situations

• They are only used for theoretical purposes

• They are not relevant outside of mathematics

• They are mainly used for historical analysis

Multiple Choice

Which of the following is NOT a condition for a binomial distribution?

• Trials are independent of each other

• Probability of success must be the same for each trial

• A fixed number of trials

• Outcomes can be more than two types

Multiple Select

Which of the following situations can be modeled by a binomial distribution?

• The number of heads obtained when an unbiased coin is tossed 10 times

• The number of black pens obtained when four pens are picked at random one at a time from a box containing 5 black pens and 15 red pens

• The number of lettuce seeds that germinate from a pack of 3 seeds, given that the probability that a lettuce seed germinates is 0.8

• All of the above

Multiple Choice

If X ~ B(10, 0.9), what is the probability that X equals 6?

• 0.0112

• 0.3874

• 0.0901

• 0.4305

Multiple Choice

If X ~ B(10, 0.9), what is the probability that X is greater than 8?

• 0.3874

• 0.1937

• 0.7361

• 0.4305

Multiple Choice

If X ~ B(10, 0.9), what is the probability that X is at least 2?

• 0.9999

• 0.9000

• 0.8100

• 0.1000

Multiple Choice

What is the probability notation used in the binomial table for the number of successes X?

• P(X ≤ x)

• P(X ≥ x)

• P(X = x)

• P(X < x)

Multiple Choice

$$P\left(X\ge3\right)$$

• 0.1579

• 0.0308

• 0.8369

• 0.1631

Multiple Choice

$$P\left(X>3\right)$$

• 0.1579

• 0.0308

• 0.9692

• 0.1631

Multiple Choice

$$P\left(X\le3\right)$$

• 0.0308

• 0.8369

• 0.9692

• 0.1631

Multiple Choice

$$P\left(X<3\right)$$

• 0.0308

• 0.8369

• 0.9692

• 0.1631

Multiple Choice

$$P\left(X=3\right)$$

• 0.0308

• 0.8369

• 0.1323

• 0.1631

Multiple Select

Which of the following statements about binomial probability is/are correct?

• The probability of exactly k successes in n trials can be found using the binomial formula.

• The mean of a binomial distribution is np.

• The variance of a binomial distribution is npq.

• The binomial distribution can only be used when the probability of success changes in each trial.

Multiple Choice

Which of the following formulas correctly represents the expected value (mean) and variance of a binomial distribution X ~ B(n, p)?

• E(X) = np, Var(X) = npq

• E(X) = npq, Var(X) = np

• E(X) = n + p, Var(X) = n - p

• E(X) = p/n, Var(X) = q/n

Multiple Choice

Let X ~ B(n, 0.22) and E(X) = 11. Find P(X = 4).

• 0.0059

• 1.5071

• 0.1358

• 0.0587

Multiple Choice

A coin is tossed 40 times. Find the mean and the standard deviation of the number of heads appeared.

• mean = 20 ,

  std dev = 10

• mean = 10 ,

  std dev = 2

• mean = 20 ,

  std dev = 3.1623

• mean = 3.1623 ,

  std dev = 20

Multiple Choice

Determine whether the following situations can be modelled by a Poisson distribution

•  The number of meteorites greater than 1 meter diameter that strike Earth in a year.

• The number of patients arriving in an emergency room between 10 and 11 pm.

• The number of photons hitting a detector in a particular time interval.

• All of the above.

Draw

An average of three cars arrive at a highway tollgate every minute. If this rate is approximately Poisson distribution what is the probability that exactly,

five cars will arrive in one minute.

Draw

An average of three cars arrive at a highway tollgate every minute. If this rate is approximately Poisson distribution what is the probability that exactly,

seven cars will arrive in five minutes

Word Cloud

If $$X\sim P_o\left(5.5\right)$$ , find $$P\left(X\ge5\right)$$

Word Cloud

If $$X\sim P_o\left(5.5\right)$$ , find $$P\left(X\le5\right)$$

Word Cloud

If $$X\sim P_o\left(5.5\right)$$ , find $$P\left(X=5\right)$$

Word Cloud

If $$X\sim P_o\left(5.5\right)$$ , find $$P\left(3\le X<8\right)$$

Multiple Choice

The number of breakdowns in a particular machine occurs at a rate of 2.5 per month. Assuming that the number of breakdowns follows Poisson distribution, find the probability that,

more than three breakdowns occur in a particular month.

• 0.2424

• 0.4562

• 0.7127

• 0.7576

Multiple Choice

The number of breakdowns in a particular machine occurs at a rate of 2.5 per month. Assuming that the number of breakdowns follows Poisson distribution, find the probability that,

less  than ten breakdowns occur in  three months period.

• 0.2236

• 0.9991

• 0.7764

• 0.9997

Multiple Choice

The number of breakdowns in a particular machine occurs at a rate of 2.5 per month. Assuming that the number of breakdowns follows Poisson distribution, find the probability that,

exactly three breakdowns occur in two months.

• 0.4562

• 0.1403

• 0.8753

• 0.7350

Multiple Choice

• mean =1.8

  variance = 1.8

• mean = 1.8

  variance = 1.8²

• mean = 1.8

  variance = 3.6

• mean = 1.8²

  variance = 1.8

Fill in the Blanks

Fill in the Blanks

Multiple Choice

In a company, the wages of a certain grade of staff are normally distributed with a standard deviation of RM 400. If 20.05% of staff earn less than RM 300 a week, 

What the percentage of staff earns more than RM500 a week?

• 0.6331

• 63.31%

• 0.3669

• 36.69%