question 14 a doctor measured serum hdl levels in her patients, and found that they were normally…
question 14 a doctor measured serum hdl levels in her patients, and found that they were normally distributed with a mean of 65.6 and a standard deviation of 3.5. find the serum hdl levels that correspond to the following z - scores. round your answers to the nearest tenth, if necessary. (a) z = -1.05 (b) z = 1.48 question help: video message instructor submit question
Answer
Answer:
(a) 61.9 (b) 70.8
Explanation:
Step1: Recall z - score formula
The z - score formula is $z=\frac{x-\mu}{\sigma}$, where $x$ is the value from the data set, $\mu$ is the mean, and $\sigma$ is the standard deviation. We can re - arrange it to solve for $x$: $x = \mu+z\sigma$. Given $\mu = 65.6$ and $\sigma = 3.5$.
Step2: Solve for (a)
For $z=-1.05$, substitute into $x=\mu + z\sigma$. So $x=65.6+( - 1.05)\times3.5=65.6 - 3.675 = 61.925\approx61.9$.
Step3: Solve for (b)
For $z = 1.48$, substitute into $x=\mu+z\sigma$. So $x=65.6+1.48\times3.5=65.6 + 5.18=70.78\approx70.8$.