If X is a normally distributed random variable with mean 14 and standa

1.	If X is a normally distributed random variable with mean 14 and standard deviation 2 then P (12 < X < 16) is
Answer» P(12 < X < 16) = 0.84134 - 0.15866 = 0.68268. Step-by-step explanation: We are GIVEN that X is a normally DISTRIBUTED random variable with mean 14 and standard deviation 2. Let X = a random variable So, X ~ Normal( $\mu=14,\sigma^{2} =2^{2}$ ) The z score PROBABILITY distribution for normal distribution is given by; Z = $\frac{X-\mu}{\sigma}$ where, $\mu$ = population mean = 14 $\sigma$ = standard deviation = 2 Now, Probability that the random variable X is between 12 and 16 is given by = P(12 < X < 16) P(12 < X < 16) = P(X < 16) - P(X $\leq$ 12) P(X < 16) = P( $\frac{X-\mu}{\sigma}$ < $\frac{16-14}{2}$ ) = P(Z < 1) = 0.84134 P(X $\leq$ 12) = P( $\frac{X-\mu}{\sigma}$ $\leq$ $\frac{12-14}{2}$ ) = P(Z $\leq$ -1) = 1 - P(Z < 1) = 1 - 0.84134 = 0.15866 The above probability is calculated by looking at the value of x = 1 in the z table which has an area of 0.84134. Therefore, P(12 < X < 16) = 0.84134 - 0.15866 = 0.68268. Learn more about normal distribution questions; https://brainly.com/question/15494018 brainly.in/question/16588240

If X is a normally distributed random variable with mean 14 and standard deviation 2 then P (12 < X < 16) is

Answer»

Step-by-step explanation:

We are GIVEN that X is a normally DISTRIBUTED random variable with mean 14 and standard deviation 2.

Let X = a random variable

So, X ~ Normal( $\mu=14,\sigma^{2} =2^{2}$ )

The z score PROBABILITY distribution for normal distribution is given by;

Z = $\frac{X-\mu}{\sigma}$

where, $\mu$ = population mean = 14

$\sigma$ = standard deviation = 2

Now, Probability that the random variable X is between 12 and 16 is given by = P(12 < X < 16)

P(12 < X < 16) = P(X < 16) - P(X $\leq$ 12)

P(X < 16) = P( $\frac{X-\mu}{\sigma}$ < $\frac{16-14}{2}$ ) = P(Z < 1) = 0.84134

P(X $\leq$ 12) = P( $\frac{X-\mu}{\sigma}$ $\leq$ $\frac{12-14}{2}$ ) = P(Z $\leq$ -1) = 1 - P(Z < 1)

= 1 - 0.84134 = 0.15866

The above probability is calculated by looking at the value of x = 1 in the z table which has an area of 0.84134.

Therefore, P(12 < X < 16) = 0.84134 - 0.15866 = 0.68268.

Learn more about normal distribution questions;

https://brainly.com/question/15494018