A polling agency is investigating the voter support for a ballot measure in an upcoming city election. The agency will select a random sample of 400 voters from one region, Region A, of the city. Assume that the population proportion of voters who would support the ballot measure in Region A is 0.46.

Required:
What is the probability that the proportion of voters in the sample of Region A who support the ballot measure is greater than 0.50?

Question

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Respuesta :

ajeigbeibraheem ajeigbeibraheem · Answer 1 · 2020-11-12T03:29:41+01:00

Answer:

0.0544

Step-by-step explanation:

From the given information;

The population proportion of the voters that would support the ballot measures in region A = 0.46

The random sample n = 400 voters

The required probability can therefore be computed as follows:

[tex]P[p_1>0.5] = P \bigg [ \dfrac{p_1-P_1}{\sqrt{\dfrac{P_1(1-P_1)}{n_1}}}>\dfrac{0.5-0.46}{\sqrt{\dfrac{0.46(1-0.46)}{400}}} \bigg][/tex]

[tex]P[p_1>0.5] = P \bigg [ Z>\dfrac{0.04}{\sqrt{\dfrac{0.46(0.54)}{400}}} \bigg][/tex]

[tex]P[p_1>0.5] = P \bigg [ Z>\dfrac{0.04}{\sqrt{6.21\times 10^{-4}}} \bigg][/tex]

[tex]P[p_1>0.5] = P \bigg [ Z>1.605 \bigg][/tex]

[tex]P[p_1>0.5] = 1- P [ Z<1.605 ][/tex]

Using the Excel Function =NORMDIST(1.605)

[tex]P[p_1>0.5] = 1- 0.9456[/tex]

[tex]P[p_1>0.5] =0.0544[/tex]

Therefore, the required probability = 0.0544