Question 1 - Normal distribution falls under which of the following categories?

Normal distribution is a kind of continuous probability distribution

Question 2 - If a particular normal curve has P(X > 2) = 0.5; what is the mode of this normal curve?

For any normal curve mean = median = mode
P(X >2) = 0.5 implies 2 is the mean.

Question 3 - Random variable X follows normal distribution, given that P(X >10) = 0.75, then calculate P(X = 10)

P(X = 10) = 0 as normal distribution is a continuous probability distribution

Question 4 - Normal curve with higher standard deviation is more sharper than the normal curve with less standard deviation (Assuming that the mean of both curves is same)

Standard deviation measures the spread or dispersion. Hence, lesser is the standard deviation sharper is the curve

Question 5 - Random variable X follows normal distribution with mean as 0. P(X > 2) = 0.2 find P(X > -2)

P(X > 2) = 0.2 and mean is 0. So, P(X < -2) = 0.2 {Normal curve is symmetric around its mean}
P(X > -2) = 1 - P(X < -2) = 0.8