Question

1. what is the z - score of a value of 115 with a mean of 100 and a standard deviation of 20? 4. the weight of newborn babies have a mean of 7.5 lbs and a standard deviation of 0.5. if a baby has a z - score of - 0.4, find it’s weight.

Explanation:

Step1: Recall z - score formula

The z - score formula is $z=\frac{x-\mu}{\sigma}$, where $x$ is the value, $\mu$ is the mean, and $\sigma$ is the standard deviation.

Step2: Solve for the first question

Given $x = 115$, $\mu=100$, and $\sigma = 20$. Substitute into the formula: $z=\frac{115 - 100}{20}=\frac{15}{20}=0.75$.

Step3: Rearrange the z - score formula for the second question

We have $z=\frac{x-\mu}{\sigma}$, and we want to find $x$. Rearranging gives $x=\mu+z\sigma$.

Step4: Solve for the second question

Given $\mu = 7.5$, $\sigma=0.5$, and $z=- 0.4$. Substitute into the formula: $x=7.5+( - 0.4)\times0.5=7.5 - 0.2=7.3$.

Answer:

1. The z - score is 0.75.
2. The weight of the baby is 7.3 lbs.