Q1. A spare part in a steel plant fails rarely, and has just failed. Historically it is known that the part failed in year 2000, 2001, 2003, 2006, 2007, 2011, and 2013. Assume the failure of the part is observed Poisson distributed. What is the part annual failure rate:

• 2.5714

• 0.3889

• 2.1667

• 0.4615

A market research team compiled the following discrete probability distribution. In this distribution, X represents the number of automobiles owned by a family. X is as follows (0,1,2,3), and P(X) is as follows (0.1, 0.1, 0.5, 0.3) respectively. The standard deviation of x is

• 0.80

• 0.89

• 1.00

• 2.00

• 2.25

At a certain workstation in an assembly line, the time required to assemble a component is exponentially distributed with a mean time of 10 minutes. Find the probability that a component is assembled in more than 12 minutes.

• 0.5034

• 0.3012

• 0.2442

• 0.2942

• 0.5084

At a certain workstation in an assembly line, the time required to assemble a component is exponentially distributed with a mean time of 10 minutes. Find the probability that a component is assembled in more than 30 minutes

• . 0.95022

• 0.04978

• 0.13530

• None of the above

Average spending of consumers at a supermarket is USD 85. It was observed that 98.9% of consumers in this supermarket have spending more than USD 77. If it is known that the distribution of the spending of the consumers follows normal distribution, determine the standard deviation of the spending

• 2.66

• 3.39

• 4.00

• 4.21

Which of the following statement is true

• For the Poisson distribution the mean and the standard deviation are the same.

• For the Poisson distribution the mean and the variance are the same.

• For the Exponential distribution the mean and the Variance are the same.

• None of the above

The National Bank operates its small branches with one teller window. On weekday mornings, arrivals to the teller window occur at random. The average inter arrival time is 2.5 minutes. Delays are expected if more than three customers arrive during any seven minute period. What is the probability that delay will occur.

• 0.3080

• 0.0002

• 0.6920

• . None of the above

Suppose 40% of all college students have a computer at home and a sample of 100 is taken. The standard deviation of the sampling distribution is

• 0.0489

• . 4.8924

• 0.0024

• 0.4890

• 0.2400

In an instant lottery, your chance of winning is 0.1. If you play the lottery 100 times and outcomes are independent, the probability that you win at least 16 percent of the time is

• 0.9772

• 0.9560

• 0.0228

• 0.0440

A random sample of size 45 is drawn from a population with a variance as 96.43. If 84.13% of the time a sample mean greater than 245.32 is obtained, the mean of the population is

• 243.86

• 246.78

• 259.69

• 230.95