Question

Just before a referendum on a school​ budget, a local newspaper polls 430 voters to predict whether the budget will pass. Suppose the budget has the support of 55​%of the voters. What is the probability that the​ newspaper's sample will lead it to predict​ defeat?

Probability is=

Answer 1

Calculations:-

Resulting in defeat, the proportion of voters in support must be less than 0.5. Assuming that the proportion of voters in support follows normal distribution, we can calculate the probability of the proportion being less than 0.5. The proportion of the voters in support = p = 0.55

The sample size of the sample is = 430

The standard deviation of the sample is given by -

s = 0.0240

Now, the proportion of the population in support follows a normal distribution with mean of 0.55 and standard deviation of 0.0240 So, the probability of mean being less than 0.5 can be calculated using the Z value of the mean as shown below -

P(p<0.5) = P(Z < {0.5-0.55} / 0.0240)

= P(Z < -2.0833)

~= P(Z< -2.08)

From the table we get the required value as

P(Z< -2.08) = 0.0188

Hence the probability that the newspapers sample will lead it to predict defeat is = 0.0188

conclusion:-

s= 0.0240

P(Z< -2.08) = 0.0188

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