Question

Math 43 Ms Abrao Midterm 2 Name Multiple Choice (3 pts. each) 1. The distribution of heights ot 150 students is approximately normally distributed with a mean of 65 inches and a standard deviation of 25 Which of the tollowing intervals would contain approx inches student imately 102 (a) 57.5 62.5" (b) 57.5" 72.5" (c) 60 70 (d) 62.5" - 67.5 2. For a uniform distribution defined on 0 x 20 where x is a continuous random variable, find P(x < 2 OR x 15) (a) 0.1 (b) 0.25 (c) 0.35 (d) 0.7 3. A simple random sample of size n 25 is drawn from a population with mean 50 and standard deviation 5. What is the standard deviation of the sampling distribution for the sample mean x? (a) 1 (b) 2 (d) 10

Answer 1

1.

102 students is 68% of the population of 150 students. By the 68-97.5-99 rule, 68% of the population is contained in the

$\mu \pm \sigma$ interval. Here $\mu =65$ and $\sigma =2.5$.

$\mu \pm \sigma=65\pm 2.5=\left ( 62.5,67.5 \right )$

The correct answer is (d) 62.5" - 67.5"

2.

The probability distribution function of continuous uniform variable X is defined as $\frac{1}{b-a}$ for the distribution defined in the limits $a\leq x\leq b$ . Here a = 0 and b = 20.

$P\left ( x<2 or x\geq 15 \right ) = P(x<2) &plus; P(x\geq 15)$

$=\frac{1}{2-0}&plus;\frac{1}{20-15}$

$=0.5&plus;0.2=0.7$

The correct option is (d) 0.7.

3.

According to the central limit theorem, the mean of the sampling distribution of sample mean $\overline{x}$ is $\mu$ and the standard deviation of the sampling distribution of sample mean is $\frac{\sigma }{\sqrt{n}}$ for the sample size n.

Standard deviation of the sampling distribution of sample mean = $\frac{5}{\sqrt{25}}=\frac{5}{5}=1$

The correct option is (a) 1.