Question

1. a coin is tossed 72 times. find the standard deviation for the number of heads that will be tossed.

a) 36 b) 18 c) 4.24 d) 6.78

1. a multiple choice quiz consists of 20 questions, each with 4 possible answers. find the mean for the number of correct answers, if a student guesses on each question.

a) 10.0 b) 5.0 c) 4.0 d) 16.0

1. a die is rolled 360 times. find the standard deviation of the number of times a 3 will be rolled

a) 21.3 b) 50 c) 7.1 d) 5.9

Explanation:

Problem 28

Step1: Identify binomial parameters

$n=72$, $p=\frac{1}{2}$, $q=1-p=\frac{1}{2}$

Step2: Apply std dev formula

$\sigma = \sqrt{npq} = \sqrt{72 \times \frac{1}{2} \times \frac{1}{2}}$

Step3: Calculate the value

$\sigma = \sqrt{18} \approx 4.24$

Problem 29

Step1: Identify binomial parameters

$n=20$, $p=\frac{1}{4}$

Step2: Apply mean formula

$\mu = np = 20 \times \frac{1}{4}$

Step3: Calculate the value

$\mu = 5.0$

Problem 30

Step1: Identify binomial parameters

$n=360$, $p=\frac{1}{6}$, $q=1-p=\frac{5}{6}$

Step2: Apply std dev formula

$\sigma = \sqrt{npq} = \sqrt{360 \times \frac{1}{6} \times \frac{5}{6}}$

Step3: Calculate the value

$\sigma = \sqrt{50} \approx 7.1$

Answer:

1. C) 4.24
2. B) 5.0
3. C) 7.1