IGNOU MTE 11 2026 - For a mesokurtic distribution with standard deviation 5, find fourth c

Question

For a mesokurtic distribution with standard deviation 5, find fourth central moment m₄.
b) The probability that a card will have a flat tyre while crossing a certain bridge is 0.00005. Find the probability that, among 10,000 cars crossing the bridge,
i) exactly two cars will have a flat tyre.
ii) at most two cards will have a flat tyre.

09 Jan 2026

Answer :

Word Count : 250

For a mesokurtic distribution, the kurtosis coefficient (\beta_2 = 3). The fourth central moment (m_4) is related to the variance (\sigma^2) by: [ \beta_2 = \frac{m_4}{\sigma^4} ] Given (\sigma = 5) and (\beta_2 = 3): [ m_4 = \beta_2 \cdot \sigma^4 = 3 \cdot 5^4 ] [ 5^4 = 5 \cdot 5 \cdot 5 \cdot 5 = 625 ] [ m_4 = 3 \cdot 625 = 1875 ] So, (m_4 = 1875). --- The probability of a flat tyre is (p = 0.00005),

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