At the amusement park, Laura paid $6.00 for a small cotton candy. Her older brother works at the park, and he told
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Answer:
a) A sample of 256 was used in this survey.
b) 45.14% probability that the point estimate was within ±15 of the population mean
Step-by-step explanation:
This question is solved using the normal probability distribution and the central limit theorem.
Normal probability distribution
When the distribution is normal, we use the z-score formula.
In a set with mean and standard deviation
, the zscore of a measure X is given by:
The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value 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. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.
Central Limit Theorem
The Central Limit Theorem estabilishes that, for a normally distributed random variable X, with mean and standard deviation
, the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean
and standard deviation
.
For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.
a. How large was the sample used in this survey?
We have that . We want to find n, so:
A sample of 256 was used in this survey.
b. What is the probability that the point estimate was within ±15 of the population mean?
15 is the bounds with want, 25 is the standard error. So
Z = 15/25 = 0.6 has a pvalue of 0.7257
Z = -15/25 = -0.6 has a pvalue of 0.2743
0.7257 - 0.2743 = 0.4514
45.14% probability that the point estimate was within ±15 of the population mean
Answer:
Adult required in the case of “a” 28 and in the case of “b” the adult requirement is 19.
Step-by-step explanation:
(a) The percentage of adult that support the change is 20 percent.
Now calculate the number of adult required.
Given p = 0.20
Use the below condition:
Since 35 adults are already there so required adults are 63 -35 = 28
(b) The percentage of adult that support the change is 25 percent.
Now calculate the number of adult required.
Given p = 0.25
Use the below condition:
Since 35 adults are already there so required adults are 54 -35 = 19 .
Answer:
The function that could be the function described is;
Step-by-step explanation:
The given parameters of the cosine function are;
The period of the cosine function = 3
The maximum value of the cosine function = 20
The minimum value of the cosine function = 0
The general form of the cosine function is presented as follows;
y = A·cos(ω·x - ∅) + k
Where;
= The amplitude = Constant
The period, T = 2·π/ω
The phase shift, = ∅/ω
k = The vertical translation = Constant
Therefore, by comparison, we have;
T = 3 = 2·π/ω
∴ ω = 2·π/3
The range of value of the cosine of an angle are;
-1 ≤ cos(θ) ≤ 1
Therefore, when A = 10, cos(ω·x - ∅) = 1 (maximum value of cos(θ)) and k = 10, we have;
y = A × cos(ω·x - ∅) + k
y = 10 × 1 + 10 = 20 = The maximum value of the function
Similarly, when A = 10, cos(ω·x - ∅) = -1 (minimum value of cos(θ)) and k = 10, we get;
y = 10 × -1 + 10 = 0 = The minimum value of the function
Given that the function is a reflection of the parent function, we can have;
A = -10, cos(ω·x - ∅) = -1 (minimum value of cos(θ)) and k = 10, to get;
y = -10 × -1 + 10 = 20 = The maximum value of the function
Similarly, for cos(ω·x - ∅) = 1 we get;
y = -10 × 1 + 10 = 0 = The minimum value of the function
Therefore, the likely values of the function are therefore;
A = -10, k = 10
The function is therefore presented as follows;
y = -10 × cos(2·π/3·x) + 10