Which of the following statements is/are true regarding the normal distribution curve?

Forty percent of the passengers who fly on a certain route do not check in any luggage. The planes on this route seat 15 passengers. For a full flight, what is the mean of the number of passengers who do not check in any luggage?

The average percentage of failure in a certain examination is 40. The probability that out of a group of 6 candidates atleast 4 passed in the examination are ________.

If for a binomial distribution b(n,p) mean = 4 and variance = 4/3, the probability, P(X ≥ 5) is equal to ________.

An experiment succeeds twice as often as it fails. The chance that in the next six trials, there shall be at least four successes is ________.

A manufacturer produces switches and experiences that 2 per cent switches are defective. The probability that in a box of 50 switches, there are atmost two defective is ________.

The parameters of the normal distribution \(f(x)=\left(\frac{1}{\sqrt{72 \pi}}\right)\)\(\frac{e^{-(x-10)^{2}}}{72}\) –∞ <  x  <  ∞ ________.

 In turning out certain toys in a manufacturing company, the average number of defectives is 1%. The probability that the sample of 100 toys there will be 3 defectives is ________.

If X ~ N(9,81) the standard normal variate Z will be ________.

Normal distribution was invented by ________.