A survey of the 12th grade students at Gaffigan High School found that 84% of the seniors have their driver’s licenses, 16% of s
1 answer:
The probability that a senior takes the bus to school every day, given that he or she has a driver’s license is 17%.
<h3>What is Probability?</h3>Probability helps us to know the chances of an event occurring.
As per the rule of conditional probability, the probability that a senior takes the bus to school every day, given that he or she has a driver’s license can be written as,
P(Have License | Takes school bus)
= (Probability the seniors have driver’s licenses and take the bus to school every day) / (Probability of Having a licenses)
= 0.14 / 0.84
= 0.16667 ≈ 17%
Hence, the probability that a senior takes the bus to school every day, given that he or she has a driver’s license is 17%.
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Answer:
0.0838 = 8.38% probability of obtaining a sample proportion less than 0.5.
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 z-score 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 p-value, we get the probability that the value of the measure is greater than X.
Central Limit Theorem
The Central Limit Theorem establishes 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.
For a proportion p in a sample of size n, the sampling distribution of the sample proportion will be approximately normal with mean and standard deviation
Proportion of 0.6
This means that
Sample of 46
This means that
Mean and standard deviation:
Probability of obtaining a sample proportion less than 0.5.
p-value of Z when X = 0.5. So
By the Central Limit Theorem
has a p-value of 0.0838
0.0838 = 8.38% probability of obtaining a sample proportion less than 0.5.