for the standard normal distribution shown on the right, find the probability of z occurring in the…

for the standard normal distribution shown on the right, find the probability of z occurring in the indicated region. (round to four decimal places as needed.)\ndraw a normal curve with a mean of 58 and a standard deviation of 11. choose the correct graph of the normal curve below.\nassume the random variable x is normally distributed with mean \\( \\mu = 81 \\) and standard deviation \\( \\sigma = 5 \\). find the indicated probability.\n\\( p ( x < 71 ) = \\) (round to four decimal places as needed.)

for the standard normal distribution shown on the right, find the probability of z occurring in the indicated region. (round to four decimal places as needed.)\ndraw a normal curve with a mean of 58 and a standard deviation of 11. choose the correct graph of the normal curve below.\nassume the random variable x is normally distributed with mean \\( \\mu = 81 \\) and standard deviation \\( \\sigma = 5 \\). find the indicated probability.\n\\( p ( x < 71 ) = \\) (round to four decimal places as needed.)

Answer

Explanation:

Step1: Calculate the z - score

The formula for the z - score is (z=\frac{x-\mu}{\sigma}). Given (\mu = 81), (\sigma=5), and (x = 71). [z=\frac{71 - 81}{5}=\frac{-10}{5}=- 2]

Step2: Find the probability using the standard normal table

We want to find (P(X\lt71)), which is equivalent to (P(Z\lt - 2)) (since (Z=\frac{X-\mu}{\sigma})). Looking up the value of (z=-2) in the standard normal table (the cumulative - distribution function of the standard normal distribution (\varPhi(z))), we know that (P(Z\lt - 2)=0.0228)

Answer:

(0.0228)