true or false - It is given that a random variable X follows normal distribution with meanσ=20andstandarddeviationμ=3. ThenP(14≤X≤26)<0.9.

## Answer<br /><br />The statement is **False**.<br /><br />Let's break down why this is the case.<br /><br />### Normal Distribution<br /><br />A random variable X that follows a normal distribution is often expressed as X ~ N(μ, σ²), where μ is the mean and σ is the standard deviation. In this case, X ~ N(20, 3²).<br /><br />### Standard Normal Distribution<br /><br />To find the probability that X falls within a certain range, we first convert X to a standard normal distribution Z ~ N(0, 1) using the formula:<br /><br />```<br />Z = (X - μ) / σ<br />```<br /><br />### Calculating the Probability<br /><br />We want to find P(14 ≤ X ≤ 26). This translates to:<br /><br />```<br />P(14 ≤ X ≤ 26) = P((14 - 20) / 3 ≤ Z ≤ (26 - 20) / 3)<br /> = P(-2 ≤ Z ≤ 2)<br />```<br /><br />According to the standard normal distribution table, the probability that Z falls within -2 and 2 is approximately 0.9545, which is greater than 0.9.<br /><br />Therefore, the statement "P(14 ≤ X ≤ 26) < 0.9" is false.