Basic Statistics2080.110 marksNumerical: normal distribution probabilityNormal distribution properties and applications
Discuss the measure properties of normal distribution. The burning time of an experimental rocket is a random variable having the normal distribution with mean 4.76 seconds and standard deviation 0.04 second respectively. What is probability that this kind of rocket will burn (i) Less than 4.68 seco
Discuss the measure properties of normal distribution. The burning time of an experimental rocket is a random variable having the normal distribution with mean 4.76 seconds and standard deviation 0.04 second respectively. What is probability that this kind of rocket will burn (i) Less than 4.68 seconds (ii) More than 4.80 seconds (iii) Anywhere from 4.70 to 4.82 seconds?μ=4.76,σ=0.04\mu = 4.76, \quad \sigma = 0.04μ=4.76,σ=0.04P(X<4.68), P(X>4.80), P(4.70<X<4.82)P(X < 4.68), ; P(X > 4.80), ; P(4.70 < X < 4.82)P(X<4.68),P(X>4.80),P(4.70<X<4.82)[10]
- Symmetry: The curve is perfectly symmetric about the mean $\mu$; the two halves are mirror images. 2. Bell-shaped: The probability density function is bell-shaped with its peak at $x = \mu$. 3. Mean = Median = Mode = $\mu$: All three measures of central tendency coincide. 4. Empirical (68-95-9...