$X$ is a random variable & has normal distribution with mean $500$ & SD is $10$. If $P(a < X < b)=0.95$ find the constants '$a$' and '$b$'
2026-04-12 18:55:47.1776020147
finding constants of a continuous probability distribution when given parameters and probability
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Hint In a standard normal distribution, $95\%$ of the area lies between $1.96$ and $-1.96$. Using the formula for z-score, we have $$-1.96 = \frac{a-500}{10}$$ $$1.96 = \frac{b-500}{10}$$