the perimeter of a rectangle parking lot is 322 m. if the length of the parking lot is 86 m, what is the width
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<span>The probability that one customer will place a take-out order is .45.
The probability that one customer will place an "eat in" order is .55.
Of 4 randomly selected customers, the probability that exactly 3 will order "take out" is given by the following:
</span>
The probability that one customer will place an "eat in" order is .55.
Of 4 randomly selected customers, the probability that exactly 3 will order "take out" is given by the following:
</span>
Answer:
15.15% probability that the sample mean will be $192,000 or more.
Step-by-step explanation:
To solve this problem, 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 random variable X, with mean and standard deviation
, a large sample size can be approximated to a normal distribution with mean
and standard deviation
In this problem, we have that:
The probability that the sample mean will be $192,000 or more is
This is 1 subtracted by the pvalue of z when X = 192000. So
By the Central Limit Theorem
has a pvalue of 0.8485.
1-0.8485 = 0.1515
15.15% probability that the sample mean will be $192,000 or more.