Question

1. in a survey, 65% of the voters support a particular referendum. if 20 voters are chosen at random, find the standard deviation of the number of voters who support the referendum.

20(.65)=13
20(.65)(.35)=√4.55=2.13

1. the following distribution is not a probability distribution because

$x$	$-2$	$-1$	$0$	$1$	$2$

a) the values of the variable are negative.
b) the probability values are not increasing.
c) the probability values do not add to 1.
d) the probability values are not discrete.

1. the following distribution is not a probability distribution because

$x$	$-2$	$-1$	$0$	$1$	$2$

a) values of the variable are negative.
b) a probability is negative.
c) the probability values do not add to 1.
d) the probability values are not discrete.

1. find the mean of the distribution shown.

$x$	$1$	$2$

a) 0.50 b) 1.50 c) 1.27 d) 1.78
.22 + 1.56 =

1. give the variance of the following distribution?

$x$	$0$	$1$	$2$	$3$	$4$

a) 1.83 b) 1.31 c) 1.25 d) 1.71
0×.20=0
1×.35=.35
2×.10=.20
3×.25=.75
4×.10=.40
$(0-1.7)^2(.20)+(1-1.7)^2(.35)+(2-1.7)^2(.10)+(3-1.7)^2(.25)+(4-1.7)^2(.10)=1.71$
1.7

1. find the mean of the distribution shown below.

$x$	$2$	$3$	$4$

a) 2.00 b) 3.08 c) 2.84 d) 3.16
2×.32=.64
3×.28=.84
4×.40=1.6
3.08

Explanation:

Question 9

Step1: Identify binomial parameters

$n=20$, $p=0.65$, $q=1-p=0.35$

Step2: Apply standard deviation formula

$\sigma = \sqrt{npq} = \sqrt{20 \times 0.65 \times 0.35}$

Step3: Calculate the value

$\sigma = \sqrt{4.55} \approx 2.13$

A valid probability distribution requires the sum of all $P(X)$ values to equal 1. Summing the given probabilities: $0.14+0.25+0.38+0.17+0.30=1.24$, which is not 1. Negative $X$ values, non-increasing probabilities, and discrete values do not invalidate a probability distribution.

A core rule of probability distributions is that all individual probabilities must be between 0 and 1 (inclusive). The given distribution has $P(X=0)=-0.18$, a negative probability, which violates this rule.

Answer:

$2.13$

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Question 10