Answer:
Hey there!
We can't compare two measurements without converting them to the same units. Thus, we use proportions to make all the values into the same unit.
, which converts to centimetres to millimetres.
12.5 cm=125 mm.
Now, we can compare the values of 125 mm and 140 mm.
Clearly, we see that 140 mm is greater than 125 mm.
Let me know if this helps :)
Answer:
39.36% probability that the proportion of couples in the sample who are racially or ethnically mixed will be greater than 0.17.
Step-by-step explanation:
For each couple, there are only two possible outcomes. Either they are mixed racially or ethnically, or they are not. This means that the binomial probability distribution is used to solve this problem.
However, we are working with samples that are considerably big. So i am going to aproximate this binomial distribution to the normal.
Binomial probability distribution
Probability of exactly x sucesses on n repeated trials, with p probability.
Can be approximated to a normal distribution, using the expected value and the standard deviation.
The expected value of the binomial distribution is:
The standard deviation of the binomial distribution is:
Normal probability distribution
Problems of normally distributed samples can be 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.
When we are approximating a binomial distribution to a normal one, we have that ,
.
In this problem, we have that:
So
When n = 100, what is the probability that the proportion of couples in the sample who are racially or ethnically mixed will be greater than 0.17?
This is 1 subtracted by the pvalue of Z when . So:
has a pvalue of 0.6064.
So there is a 1-0.6064 = 0.3936 = 39.36% probability that the proportion of couples in the sample who are racially or ethnically mixed will be greater than 0.17.
Answer:
The total golf balls Jack has now in terms of expression is as below
Where a is total number of balls and b is number of balls in each bag.
Step-by-step explanation:
Solution:
let a be the total number of balls and b is the number of balls in each bag.
Number of bags is 3.
So total number of balls before the friend gave is
Now the friend has given him 6 more golf balls then the total number of balls will become 3b + 6.
Therefore, the required expression is