Complete the squares so that the differences shown on the outside are correct
2 answers:
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Answer:
1) 0.5 or 50%.
2) Order does not matter: 3,003 combinations.
Order matters: 360,360 permutations.
Step-by-step explanation:
1) The probability of drawing either a purple or a blue chip is the sum of both individual probabilities:
the probability that a blue or a purple chip will be drawn is 0.5 or 50%.
2)
a) Choose 5 items from a total of 15 items when order does not matter:
b) Choose 5 items from a total of 15 items when order matters:
<u>ANSWER: </u>
In a data set with a range of 55.4 to 105.4 and 400 observations.86 lies in the 49th percentile.
<u>SOLUTION: </u>
Given, in a data set with a range of 55.4 to 105.4 and 400 observations.
There are 176 observations below the value of 86, and we need to find the percentile for 86.
We know that, percentile formula =
Percentile of 86 =
Since, we cancelled 400 with 100 we get 4 , hence above expression becomes,
= 49
So, percentile of 86 = 49
Hence, 86 lies in the 49th percentile.
Answer:
a) P(12.99 ≤ X ≤ 13.01) = 0.3840
b) P(X ≥ 13.01) = 0.3075
Step-by-step explanation:
To solve this question, we need to understand the normal probability distribution and the cental limit theorem.
Normal probability distribution
Problems of normally distributed samples are solved using 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.
In this problem, we have that:
(a) Calculate P(12.99 ≤ X ≤ 13.01) when n = 16.
Here we have
This probability is the pvalue of Z when X = 13.01 subtracted by the pvalue of Z when X = 12.99.
X = 13.01
By the Central Limit Theorem
has a pvalue of 0.6915
X = 12.99
has a pvalue of 0.3075
0.6915 - 0.3075 = 0.3840
P(12.99 ≤ X ≤ 13.01) = 0.3840
(b) How likely is it that the sample mean diameter exceeds 13.01 when n = 25?
P(X ≥ 13.01) =
This is 1 subtracted by the pvalue of Z when X = 13.01. So
has a pvalue of 0.6915
1 - 0.6915 = 0.3075
P(X ≥ 13.01) = 0.3075