Question

1-What are the three major differences between a normal distribution and a binomial
distribution?

2- Why is the Normal Distribution called "Normal"?

3- What are examples of exponentially distributed random variables in real life?

Answer 1

1-What are the three major differences between a normal distribution and a binomial distribution?

Normal distribution Binomial distribution

It is continuous distribution. It is discrete distribution

Here sample size is large Here sample size is small

Mean of the distribution is population mean Mean of the distribution is proportion.

2- Why is the Normal Distribution called "Normal"?

Initially the normal distribution was called as "Gaussian distribution" after the famous mathematician ”GAUSS”. The name normal was attributed later due to great statistician Karl E. Pearson, who said,

Many years ago [in 1893] I called the Laplace-Gaussian curve the normal curve, which name, while it avoids the international question of priority, has the disadvantage of leading people to believe that all other distributions of frequency are in one sense or another abnormal.”

3- What are examples of exponentially distributed random variables in real life?

i) Waiting time of two consecutive customers who are come at telephone booth for calling someone.

ii) amount of time (beginning now) until an earthquake occurs

iii) amount of time, in months, a car battery lasts.