Question

question #3 iq scores are normally distributed with mean μ = 100 and standard deviation σ = 15. calculate the standard deviation of the sampling distribution using a sample size of 50. 21.20 2.12 0.30 3.00 question #4 for a population that is distributed normally with a mean of 1.9 and a standard deviation of 0.8, calculate p(x < 3.5). .9772 .9433 .1247 .2013

Explanation:

Question #3

Step1: Recall the formula for standard deviation of sampling distribution

The formula for the standard deviation of the sampling distribution (also known as the standard error) is $\sigma_{\bar{x}}=\frac{\sigma}{\sqrt{n}}$, where $\sigma$ is the population standard - deviation and $n$ is the sample size.

Step2: Substitute the given values

We are given that $\sigma = 15$ and $n = 50$. So, $\sigma_{\bar{x}}=\frac{15}{\sqrt{50}}$.
Calculate $\sqrt{50}\approx7.071$. Then $\frac{15}{7.071}\approx2.12$.

Step1: Calculate the z - score

The z - score is calculated using the formula $z=\frac{x-\mu}{\sigma}$, where $x$ is the value from the data set, $\mu$ is the mean, and $\sigma$ is the standard deviation. Here, $\mu = 1.9$, $\sigma=0.8$, and $x = 3.5$.
So, $z=\frac{3.5 - 1.9}{0.8}=\frac{1.6}{0.8}=2$.

Step2: Find the probability using the standard normal distribution table

We want to find $P(X < 3.5)$, which is equivalent to $P(Z < 2)$ when we standardize. Looking up the value of $P(Z < 2)$ in the standard - normal distribution table, we get $P(Z < 2)=0.9772$.

Answer:

2.12

Question #4