Four coins are tossed simultaneously. What is the probability of getting
a) atleast 2 heads
b) atmost 2 heads.

20% of the bolts produced in a factory are found to be defective. Find the probability that in a sample of 10 bolts chosen at random exactly 2 will be defective using
(i) Binomial distribution
(ii) Poisson distribution (e^-2 = 0.1353)

The mean weight of 500 male students in a certain college is 151 pounds and the S.D is 15 pounds. Assuming the weights are normally distributed, find how many students weight
(i) between 120 and 155 pounds
(ii) more than 185 pounds.

If the height of 300 students are normally distributed with mean 64.5 inches and standard deviation 3.3 inches find the height below which 99% of the student lie?

Marks in an aptitude test given to 800 students of a school was found to be normally distributed 10% of the students scored below 40 marks and 10% of the students scored above 90 marks. Find the number of students scored between 40 and 90?

If x follows binomial distribution with mean 4 and variance 2, find \(P(|X-4| \leq 2)\).

The sum and product of the mean and variance of a binomial distribution are 24 and 128 respectively.Find their distribution. 

A pair of dice in thrown 7 times. If getting a total of 7 is considered a success, what is the probability of
(i) no success
(ii) 6 success
(iii) atleast 6 successes
(iv) atmost 6 successes

A die is thrown 6 times. If "getting an odd number" is a success what is the probability of
(i) 5 successes
(ii) atleast 5 success
(iii) at most 5 successes
(iv) atleast one success x = 0 
(v) no success

For a Binomial distribution with parameters n = 5 and p = 0.3, find the probability of getting
(i) atleast 3 successes
(ii) at most 3 successes.

Find the probability that atmost 5 defective fuses wil be found in a box of 200 fuses if experience shows that 2 percent of such fuses are defective. (e^-4 = 0.0183)

The number of accidents in a year attributed to taxi drivers in a city follows poisson distribution with mean 3. Out of 1000 taxi drivers find
(i) the approximate number of drivers with no accident in a year
(ii) more than 3 accidents in a year

An insurance company insured 4000 people against loss of both eyes in car accident. Based on previous data, the rates were computed on the assumption that on the average 10 person in 1,00,000 will have car accidents cactch year that result in this type of injury. What is the probability that more than 3 of the injured will collect on their policy in a given year(e^-0.4 = 0.6703)

What is the probability that Z
(a) lies between 0 and 1.83
(b) is greater than 1.54
(c) is greater than -0.86
(d) lies between 0.43 and 1.12
(e) is less than 0.77

If X is a normal variable with mean 100 and variance 36. Find
(i) P(X > 112)
(ii) P(X < 106)
(iii) P(94