Question

Assume the random variable x is normally distributed with mean μ = 80 and standard deviation σ = 4. Find the indicated probability.
P(x < 72) = _____ (round to four decimal places as needed).

Answer 1

Answer:

0.2278

Step-by-step explanation:

z = (x-μ)/σ,

where x is the raw score

μ is the population mean

σ is the population standard deviation

z => 72 - 80/4

= -2

Probability value from Z-Table:

P(x ≤ 72) = P(x = 72) => P(x < 72)

0.02275

Approximately =>0.2278

Answer 2

The probability of the calculated value is " 0.0227501", its calculation can be defined as follows:

Normal distribution calculation:

Mean $(\mu)= 80$

Standard Deviation $(\sigma)= 4$

Since we know that

$\to Z_{\text{score}} =\frac{x-\mu}{\sigma}$

a)$x = 72$

$\to \frac{72-80}{4}=\frac{-8}{4}= -2$

so,

$P(x < 72) = P(z < -2) =0.0227501$

PS: you have to refer z score table to find the final probabilities.

Find out more about the p-value here:

brainly.com/question/14723549