Slader "Two balls are chosen randomly from an urn containing 8 white, 4 black, and 2 orange balls. Suppose that we win $2 for ea
ch black ball selected and we lose $1 for each white ball selected. Let X denote our winnings."
What are the probabilities associated with each possible value for X?
What are the probabilities associated with each possible value for X?
1 answer:
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Answer:
B. Mean = 1.6 years, standard deviation = 0.92 years, shape: approximately Normal.
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 normal distributions 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.
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.
Subtraction of normal variables:
When we subtract normal variables, the mean is the subtraction of the means, while the standard deviation is the square root of the sum of the variances.
35 gas ovens
A consumer group has determined that the distribution of life spans for gas ovens has a mean of 15.0 years and a standard deviation of 4.2 years. This means that:
40 electric ovens.
The distribution of life spans for electric ovens has a mean of 13.4 years and a standard deviation of 3.7 years.
Which of the following best describes the sampling distribution of barXG - bar XE, the difference in mean life span of gas and electric ovens?
By the Central Limit Theorem, the shape is approximately normal.
Mean:
Standard deviation:
So the correct answer is given by option b.