Question

The number of calories burned at the gym is normally distributed with a mean of 425 and a standard deviation of 51. Find the Z-score for each data value.
a.)268 b.)512 c.)450

Answer 1

Answer:

(a) -3.708

(b) 1.706

(c) 0.490

Step-by-step explanation:

The z-score of normal distribution is given as:

$z=\frac{x-\mu}{\sigma}$

(a)

Given:

Score is, $x=268$

Mean value is, $\mu =425$

Standard deviation is, $\sigma = 51$

z-score is, $z=\frac{268-425}{51}=\frac{-157}{51}=-3.078$

(b)

Given:

Score is, $x=512$

Mean value is, $\mu =425$

Standard deviation is, $\sigma = 51$

z-score is, $z=\frac{512-425}{51}=\frac{87}{51}=1.706$

(c)

Given:

Score is, $x=450$

Mean value is, $\mu =425$

Standard deviation is, $\sigma = 51$

z-score is, $z=\frac{450-425}{51}=\frac{25}{51}=0.490$