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

(a) -3.708

(b) 1.706

(c) 0.490

Explanation:

The z-score of normal distribution is given as:

`z=(x-\mu)/(\sigma)`

(a)

Given:

Score is,
`x=268`

Mean value is,
`\mu =425`

Standard deviation is,
`\sigma = 51`

z-score is,
`z=(268-425)/(51)=(-157)/(51)=-3.078`

(b)

Given:

Score is,
`x=512`

Mean value is,
`\mu =425`

Standard deviation is,
`\sigma = 51`

z-score is,
`z=(512-425)/(51)=(87)/(51)=1.706`

(c)

Given:

Score is,
`x=450`

Mean value is,
`\mu =425`

Standard deviation is,
`\sigma = 51`

z-score is,
`z=(450-425)/(51)=(25)/(51)=0.490`