Antonio used 1613 cups of flour to make banana bread. The recipe for one loaf of banana bread calls for 213 cups of flour. What
1 answer:
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Answer: $9 per hour at his job as a cashier and $8 per hour at his job delivering newspapers.
Step-by-step explanation:
1. Let's call the amount he got paid per hour at his job as a cashier: .
Let's call the amount he got paid per hour at his job delivering newspapers: .
2. Keeping on mind the information given in the problem above, you can make the following system of equations:
3. You can solve it by applying the Substitution method, as following:
- Solve for one of the variables from one of the equations and substitute it into the other equation to solve for the other variable and calculate its value.
- Substitute the value obtained into one of the original equations to solve for the other variable and calculate its value.
4. Therefore, you have:
Then:
Finally:
Therefore he got paid $9 per hour at his job as a cashier and $8 per hour at his job delivering newspapers.
Answer:
0.43% probability that the mean IQ score of 50 randomly selected people will be more than 23
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 question:
What is the probability that the mean IQ score of 50 randomly selected people will be more than 23
This is 1 subtracted by the pvalue of Z when X = 23. So
By the Central Limit Theorem
has a pvalue of 0.9957
1 - 0.9957 = 0.0043
0.43% probability that the mean IQ score of 50 randomly selected people will be more than 23