CNNBC recently reported that the mean annual cost of auto insurance is 954 dollars. Assume the standard deviation is 271 dollars. You take a simple random sample of 96 auto insurance policies.
Find the probability that a single randomly selected value is less than 969 dollars.
Write your answers as numbers accurate to 4 decimal places.
The Z-score of a random variable X is defined as follows:
Here, are the mean and standard deviation of X, respectively.
Take into account the X random variable, which represents the annual cost of car insurance.
The information provided indicates that X has a normal distribution, with a mean of 954 and a standard deviation of 271. The sample size, n is 96.
The likelihood that any given value chosen at random is less than 969 dollars is
(Using standard normal table: )
Thus, there is a 0.5221 percent chance that a single randomly chosen value will be less than 969 dollars.
Answer is given below (on video)
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