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Assignment Task :
The normal rate of infection of a certain disease in animals is known to be 25 percent. In an experiment with 6 animals injected with a new vaccine it was observed that none of the animals caught the injection. Calculate the probability of the observed result with a new vaccine.
On an average, one in 400 items is defective. If the items are packed in boxes of 100, what is the probability that any given box of items will contain: (i) no defectives, (ii) less than two defectives, (iii) one or more defectives and (iv) more than three defectives.
A workshop produces 2000 units of an item per day. The average weight of units is 130 kg with a standard deviation of 10 kg. Assuming normal distribution, how many units are expected to weigh less than 142 kg?
If the probability of defective bolts be 1/10, find the following for the binomial distribution of defective bolts in a total of 400 bolts: (a) mean, (b) standard deviation. (c) What is the probability of atmost 50 defective bolts. (d) What is the probability of 50 to 100 defective bolts.
The amount of time consumed by an individual at a bank ATM is found to be normally distributed with mean 130 seconds and standard deviation 45 seconds.
What is the probability that a randomly selected individual will consume less than 100 seconds at the ATM?
What is the probability that a randomly selected individual will spend between 2 to 3 minutes at the ATM?
Within what length of time do 20 percent of individuals complete their job at the ATM?
What is the least amount of time required for individuals with top 5 percent of required time?
The incidence of occupational disease in an industry is such that the workers have a 20 % chance of suffering from it. What is the probability that out of 6 workers 4 or more will suffer from disease?
The incidence of occupational disease in an industry is such that the workers have 20% chance of suffering from it. What is the probability that out of six workers 4 or more will come in contact of the disease?
10 % bolts produced by a machine are defective. Find the probability of the following when they are checked at random by examining samples of 5:
None is defective
One is defective
At most one is defective
Bits are sent over a communications channel in packets of 12. If the probability of a bit being corrupted over this channel is 0:1 and such errors are independent, what is the probability that no more than 2 bits in a packet are corrupted?
If 6 packets are sent over the channel, what is the probability that at least one packet will contain 3 or more corrupted bits?
Let X denote the number of packets containing 3 or more corrupted bits. What is the probability that X will exceed its mean by more than 2 standard deviations?
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