Marcy has 567 earmuffs in stock .If she can put 18 earmuffs on each shelf about how many shelves does she need for all the earmu
1 answer:
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Answer:
[0.875;0.925]
Step-by-step explanation:
Hello!
You have a random sample of n= 400 from a binomial population with x= 358 success.
Your variable is distributed X~Bi(n;ρ)
Since the sample is large enough you can apply the Central Limit Teorem and approximate the distribution of the sample proportion to normal
^ρ≈N(ρ;(ρ(1-ρ))/n)
And the standarization is
Z= ^ρ-ρ ≈N(0;1)
√(ρ(1-ρ)/n)
The formula to estimate the population proportion with a Confidence Interval is
[^ρ ± *√(^ρ(1-^ρ)/n)]
The sample proportion is calculated with the following formula:
^ρ= x/n = 358/400 = 0.895 ≅ 0.90
And the Z-value is ≅ 1.65
[0.90 ± 1.65 * √((0.90*0.10)/400)]
[0.875;0.925]
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Answer:
Probability that the proportion of Americans who can order a meal in a foreign language is greater than 0.5 is 0.19766.
Step-by-step explanation:
We are given that according to a study done by Wake field Research, the proportion of Americans who can order a meal in a foreign language is 0.47.
Suppose a random sample of 200 Americans is asked to disclose whether they can order a meal in a foreign language.
<em>Let </em><em> = sample proportion of Americans who can order a meal in a foreign language</em>
The z-score probability distribution for sample proportion is given by;
Z = ~ N(0,1)
where, = sample proportion
p = population proportion of Americans who can order a meal in a foreign language = 0.47
n = sample of Americans = 200
Probability that the proportion of Americans who can order a meal in a foreign language is greater than 0.5 is given by = P( > 0.50)
P( > 0.06) = P(
>
) = P(Z > 0.85) = 1 - P(Z
0.85)
= 1 - 0.80234 = <u>0.19766</u>
<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 = 0.85 in the z table which has an area of 0.80234.</em>
Therefore, probability that the proportion of Americans who can order a meal in a foreign language is greater than 0.5 is 0.19766.