A number decreased by 4 equals -12. What is the number? _____
1 answer:
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Answer:
Klorina's rate in still water is 4.5 km/h
Current's rate is 0.5 km/h
Step-by-step explanation:
Let
x km/h = Klorina's rate in still water
y km/h = current's rate
<u>With the current (current helps):</u>
Distance = 10 km
Time = 2 hours
Rate = x + y km/h
<u>Against the current:</u>
Distance = 8 km
Time = 2 hours
Rate = x - y km/h
Divide both equations by 2:
Add these equations:
Subtract these two equations:
Answer:
0.0228 = 2.28% probability that the average score of the 64 golfers exceeded 76.
Step-by-step explanation:
To solve this question, we need to understand the normal probability distribution and the central 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:
Find the probability that the average score of the 64 golfers exceeded 76.
This is 1 subtracted by the pvalue of Z when X = 64.
By the Central Limit Theorem
has a pvalue of 0.9772
1 - 0.9772 = 0.0228
0.0228 = 2.28% probability that the average score of the 64 golfers exceeded 76.