Answer: b. Her weight is 1.5 standard deviations below average.
Step-by-step explanation:
Given : A woman is told her weight has a standard score (z-score) of -1.5.
Let x denotes a random variable that represents the weight of woman.
Since , [tex]z=\dfrac{x-\mu}{\sigma}[/tex]
, where [tex]\mu[/tex] = Population mean and [tex]\sigma[/tex] = Population standard deviation.
Put z= -1.5 in this , we get
[tex]-1.5=\dfrac{x-\mu}{\sigma}[/tex]
i.e. [tex]-1.5\sigma=x-\mu[/tex]
i.e. [tex]x=\mu-1.5\sigma[/tex]
It means , x is 1.5 standard deviations below the mean value.
This means that: Her weight is 1.5 standard deviations below average.
Hence, the correct answer is b. Her weight is 1.5 standard deviations below average.
