Answer:
The margin of error that corresponds to a 95% confidence interval is 4.96.
Step-by-step explanation:
We have the standard error(which is the same as the standard deviation of the sample), so we use the students t-distribution to solve this question.
The first step to solve this problem is finding how many degrees of freedom, we have. This is the sample size subtracted by 1. There are 6 days, so
df = 6 - 1 = 5
95% confidence interval
Now, we have to find a value of T, which is found looking at the t table, with 35 degrees of freedom(y-axis) and a confidence level of ). So we have T = 2.5706
The margin of error is:
M = T*s = 2.5706*1.93 = 4.96
The margin of error that corresponds to a 95% confidence interval is 4.96.
A function assigns the values. The graph can be plotted as shown below.
<h3>What is a Function?</h3>A function assigns the value of each element of one set to the other specific element of another set.
Given the function, g(x) = -3(1/2)ˣ, therefore, the value of g(x) can be written as,
g(x) = -3(1/2)ˣ
g(-2) = -3(1/2)² = -0.75
g(-1) = -3(1/2)¹ = -1.5
g(0) = -3(1/2)⁰ = -3
g(1) = -3(1/2)¹ = -1.5
Hence, the graph can be plotted as shown below.
Learn more about Function:
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Answer:
The probability that Polly's Sample will give a result within 1% of the value 65% is 0.6424
Step-by-step explanation:
The variable that assigns the value 1 if a person had its original major and 0 otherwise is a Bernoulli variable with paramenter 0.65. Since she asked the question to 1850 people, then the number of students that will have their original major is a Binomial random variable with parameters n = 1850, p = 0.65.
Since the sample is large enough, we can use the Central Limit Theorem to approximate that random variable to a Normal random variable, which we will denote X.
The parameters of X are determined with the mean and standard deviation of the Binomal that we are approximating. The mean is np = 1850*0.65 = 1202.5, and the standard deviation is √np(1-p) = √(1202.5*0.35) = 20.5152.
We want to know the probability that X is between 0.64*1850 = 1184 and 0.66*1850 = 1221 (that is, the percentage is between 64 and 66). In order to calculate this, we standarize X so that we can work with a standard normal random variable W ≈ N(0,1). The standarization is obtained by substracting the mean from X and dividing the result by the standard deviation, in other words
The values of the cummulative function of the standard normal variable W, which we will denote are tabulated and they can be found in the attached file.
Now, we are ready to compute the probability that X is between 1184 and 1221. Remember that, since the standard random variable is symmetric through 0, then \phi(-z) = 1-\phi(z) for each positive value z.
Therefore, the probability that Polly's Sample will give a result within 1% of the value 65% is 0.6424.
Answer:
The lengths of the sides of the playground are 14 feet, 6 feet, 7 feet
Step-by-step explanation:
At first, let us find the perimeter of the playground
∵ Perimeter of a triangle is P = S1 + S2 + S3
∵ The sides of the triangular playground are (2x) ft, (x - 1) ft, and x ft
∴ S1 = 2x, S2 = x - 1, S3 = x
→ Substitute them in the rule of the perimeter above
∵ P = 2x + x - 1 + x
→ Add the like terms
∴ P = (2x + x + x) - 1
∴ P = 4x - 1
∵ The perimeter of this playground is 27 feet
∴ P = 27
→ Equate the two values of P
∴ 4x - 1 = 27
→ Add 1 to both sides
∴ 4x - 1 + 1 = 27 + 1
∴ 4x = 28
→ Divide both sides by 4
∵ =
∴ x = 7
→ Substitute the value of x in each side to find their lengths
∵ S1 = 2(7)
∴ S1 = 14 feet
∵ S2 = 7 - 1
∴ S2 = 6 feet
∵ S3 = 7 feet
∴ The lengths of the sides of the playground are 14 feet, 6 feet, 7 feet