The score on the GMAT is normally distributed with mean 560 and standard deviation 120. Suppose n = 25 randomly selected students take the GMAT on the same day.
What is the probability that one randomly selected student scores above 575 on the GMAT?
From the Z score calculator available online [ https://www.fourmilab.ch/rpkp/experiments/analysis/zCalc.html ].
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Alternatively (Online Stat Book) [ http://onlinestatbook.com/2/calculators/normal_dist.html ].
Therefore,
Describe the sampling distribution of the sample mean for the 25 students.
Since the original sample size is normally distributed, the sampling distribution of the mean sample for the 25 students will also be normally distributed. Generally, the sampling distribution will be normally distributed for any sample size if the original population is normally distributed.
What is the probability that a random sample of 25 students has a mean GMAT score that is less than 575?
Using the Online Stat Book,
What is the probability that a random sample of 25 students has a mean GMAT score that is 575 or above?
In the United States, the year each coin was minted is printed on the coin. To find the age of a coin, simply subtract the current year from the year printed on the coin. The ages of circulating pennies are right skewed. Most circulating pennies were minted relatively recently, and extremely old pennies are rare. Assume the ages of circulating pennies have a mean of 30 years and a standard deviation of 9.9 years.
a. Based on the information given, can we determine the probability that a randomly selected penny is over 10 years old?
Based on the information provided, we cannot determine the probability that a randomly selected penny is over 10 years old. This is because the population is not normally distributed.
b. What is the probability that a random sample of 40 circulating pennies has a mean less than 25 years?
Using the Online Stat Book,
c. What is the probability that a random sample of 40 circulating pennies has a mean greater than 25 years?
What is the probability that a random sample of 40 circulating pennies has a mean greater than 32 years? Would this be unusual? Why or why not?
Therefore,
This would not be unusual. We call anything “unusual” if it happens less than 5% of the time.
