Question

Suppose a large shipment of cell phones contain 21% defective. If the sample of size 204 is selected, what is the probability that the sample proportion will differ from the population proportion by less than 4% round your answer to four decimal places

224

likes
1120 views

Answer to a math question Suppose a large shipment of cell phones contain 21% defective. If the sample of size 204 is selected, what is the probability that the sample proportion will differ from the population proportion by less than 4% round your answer to four decimal places

Expert avatar
Cristian
4.7
111 Answers
The mean of the sampling distribution of the proportion is equal to the population proportion (p). So, μ = p = 0.21. The standard deviation of the sampling distribution of the proportion (σp̂) is given by the formula: σp̂ = sqrt [ p(1 - p) / n ] σp̂ = sqrt [ 0.21 * (1 - 0.21) / 204 ] ≈ 0.0285 z = (0.04 - 0) / 0.027 ≈ 1.40265 Using a standard normal distribution table, we find that the probability of a z-score being less than 1.40265 is approximately 0.91964 P = 1 - 2 * (1 - 0.91964) = 0.83928 So, the probability that the sample proportion will differ from the population proportion by less than 4% is approximately 0.8393 or 83.93% when rounded to four decimal places.

Frequently asked questions (FAQs)
Math question: Graph the inequality y > 2x - 3. Find the solution set and represent it on a coordinate plane. Are there infinitely many solutions?
+
Math question: What are the characteristics of a parabola's graph?
+
What is the probability of rolling a 6-sided die and getting a prime number?
+
New questions in Mathematics
5 . {2/5 + [ (8/-9) - (1/-7) + (-2/5) ] ÷ (2/-5)} . 8/15
A hotel in the Algarve had to offer 1 week of vacation to one of its employees as an Easter gift in a random choice. It is known that 80 people work in this hotel unit, 41 of whom are Portuguese and 39 are foreign nationals. There are 14 Portuguese men and 23 foreign women. Using what you know about conditional probability, check the probability that the gift was offered to a Portuguese citizen, knowing that it was a woman.
STUDENTS IN A CLASS LEARN ONLY ONE FOREIGN LANGUAGE. two-sevenths of the students learn German, half of the students learn Spanish, and the remaining six students learn Italian. what is the number of students in this class? detail your reasoning carefully.
Calculate the equation of the tangent line ay=sin(x) cos⁡(x)en x=π/2
Divide 22 by 5 solve it by array and an area model
How many different ways can a psychology student select 5 subjects from a pool of 20 subjects and assign each one to a different experiment?
-27=-7u 5(u-3)
Determine the minimum degree that an algebraic equation can assume knowing that it admits 2 as a double root and -i as a triple root
Calculate the minimum size of a simple random sample assuming a sampling error of 5% assuming that the population size is 100 elements
There are 3 orchards, a, b and c. Orchard a has 60 fewer trees than orchard b orchard c has 3 times as many trees as orchard b. If the three orchards have 430 trees altogether, how many trees does orchard c have?
Use a pattern approach to explain why (-2)(-3)=6
9 x² + 2x + 1 = 0
9.25=2pi r solve for r
A car travels 211 miles on 15 gallons of gasoline. The best estimate of the car’s miles per gallon is?
How to factorise 5y^2 -7y -52
In poker, a full house consists of five cards, where two of the cards have the same number (or letter) and the remaining three also have the same number (or letter) as each other (but not as the previous two cards). Use a search engine or Wikipedia to understand the concept better if necessary. In how many different ways can one obtain a full house?
Find the vertex F(x)=x^2-10x
The average weekly earnings in the leisure and hospitality industry group for a re‐ cent year was $273. A random sample of 40 workers showed weekly average ear‐ nings of $285 with the population standard deviation equal to 58. At the 0.05 level of significance can it be concluded that the mean differs from $273? Find a 95% con‐ fidence interval for the weekly earnings and show that it supports the results of the hypothesis test.
To paint a 250 m wall, a number of workers were employed. If the wall were 30 m longer, 9 more workers would be needed. How many were employed at the beginning?
Kayla started a book club at her school. The number of girls in the book club was one more than twice the number of boys. If there are 15 girls in the book club, how many boys are in the club?