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Answer:
Probability that the sample proportion will be greater than 0.5 is 0.8133.
Step-by-step explanation:
We are given that the a particular candidate for public office is in fact favored by p = 48% of all registered voters. A polling organization is about to take a simple random sample of voters and will use the sample proportion to estimate p.
Suppose that the polling organization takes a simple random sample of 500 voters.
<em>Let </em><em> = sample proportion</em>
The z-score probability distribution for sample proportion is given by;
Z = ~ N(0,1)
where, = sample proportion
p = population proportion = 48%
n = sample of voters = 500
The Z-score measures how many standard deviations the measure is away from the mean. After finding the Z-score, we look at the z-score table and find the p-value (area) associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X.
So, probability that the sample proportion will be greater than 0.5 is given by = P( > 0.50)
P( > 0.50) = P(
<
) = P(Z < 0.89) = 0.8133
<em>Now, in the z table the P(Z </em><em> x) or P(Z < x) is given. So, the above probability is calculated by looking at the value of x = 0.89 in the z table which has an area of 0.8133.</em>
Therefore, probability that the sample proportion will be greater than 0.50 is 0.8133.
Answer:
5B; 7B; 1,024; see answer
Step-by-step explanation:
5.
We can see from the table that
a1 = 5
a2= 5·2 = 10
a3= 5·2·2 = 5·2² = 20
a4 = 5·2·2·2 = 5·2³ = 40
...
7.
Is given that the filter removes 90% of contaminated air
after run 1 :
100% air
90% contamination removed for 100% air
100% is 10%+10%+10%+10%+10%+10%+10%+10%+10%+10%
10% is still contaminated air
after run 2:
10% air
90% contamination removed for 10% air
10% is 1%+1%+1%+1%+1%+1%+1%+1%+1%+1%
1% is still contaminated air
after run 3:
1% air
90% contamination removed for 1% air
1% is .1%+.1%+.1%+.1%+.1%+.1%+.1%+.1%+.1%+.1%
<u>.1% is still contaminated air</u>
11.
Figure 1 = 1 piece
Figure 2 = 4 pieces
Figure 3 = 4² = 16
...
12.
-we know that the coefficients should be 1, 6, 15, 20, 15, 6, 1
-we start with c to the lowest power 0 and d to the highest power 6 and end with d to the lowest power 0 and c to the highest power 6
-we simplify to have the final answer: