In a recent year, about 22% of Americans 18 years and older are single. What is the probability that in a random sample of 200 Americans 18 or older more than 30 are single? (Hint: use binomial to normal approximation techniques) Round your z-score to 2 decimal places before referencing table E. Then provide answer out to 4 decimal places.
Using the normal approximation to the binomial, it is found that there is a 0.0107 = 1.07% probability that more than 30 are single.
Normal Probability DistributionThe z-score of a measure X of a normally distributed variable with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex] is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The z-score measures how many standard deviations the measure is above or below the mean. Looking at the z-score table, the p-value associated with this z-score is found, which is the percentile of X.The binomial distribution is the probability of x successes on n trials, with p probability of a success on each trial. It can be approximated to the normal distribution with [tex]\mu = np, \sigma = \sqrt{np(1-p)}[/tex].In this problem, the proportion and the sample size are, respectively, p = 0.22 and n = 200, hence:
[tex]\mu = np = 200(0.22) = 44[/tex]
[tex]\sigma = \sqrt{np(1 - p)} = \sqrt{200(0.22)(0.78)} = 5.8583[/tex]
The probability that more than 30 are single, using continuity correction, is P(X > 30.5), which is 1 subtracted by the p-value of Z when X = 30.5, hence:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{30.5 - 44}{5.8583}[/tex]
Z = -2.3
Z = -2.3 has a p-value of 0.0107.
0.0107 = 1.07% probability that more than 30 are single.
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If f(x) and it’s inverse function,f-1(x), are both potted on the same coordinate plane, where point of intersection?
Define award package. What does it include?
Answer:
Your award letter will list the types and amounts of aid being offered. Aid may be a grant, a scholarship, a loan, work-study—or a combination of these aid types. The award letter should also include: A breakdown of the college's cost of attendance (COA)
Answer:
Your award letter will list the types and amounts of aid being offered. Aid may be a grant, a scholarship, a loan, work-study—or a combination of these aid types. The award letter should also include: A breakdown of the college's cost of attendance (COA)
Explanation:
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BRAIN LESS ANSWER
PLS HELP ASAP! BRAINLIEST IF CORRECT!! The trait for flower color in a plant has red and white alleles. The red color is the dominant trait. What is the phenotypic ratio for a cross between plants with red (Rr) flowers and white (rr) flowers?
4 red : 0 white
3 red : 1 white
2 red : 2 white
0 red : 4 white
Answer:
Its 4 red: 0 white
Explanation:
look at a RrRr punnet square, then it shows the ratio.
R R
r Rr Rr
r Rr Rr
the square shows that all the plants will be red because if a trait is recessive, it needs to be shown in both parents for the offspring to have it. All offspring will carry this trait, but it will not show.
Which will not help you earn more interest in a savings account?
A. Withdrawing money from the account on a regular basis
B. Keeping your money in the account for a long time
C. Depositing money into the account on a regular basis
D. A high interest rate
Answer:A
Explanation:AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAA