Finding the Probability of the z-Score Range
In a certain city, the average monthly temperature is 30 degrees Celsius with a standard deviation of 3 degrees. What is the probability that the average temperature for a randomly selected month falls between 27 and 33 degrees?
Finding the Probability of a Range in a Nonstandard Normal Distribution
A set of data is normally distributed with a mean of 100 and a standard deviation of 15. What is the probability that a randomly selected data point will be between 85 and 115?
Finding the z-Score Using the Table
Suppose the grades in a statistics class follow a normal distribution with a mean of 75 and a standard deviation of 8. What is the z-score for a grade of 85?
Finding a t-Value for a Confidence Level
In a population where the mean is \( \mu = 100 \) and the standard deviation is \( \sigma = 15 \), we are interested in finding the t-value for a 95% confidence level for a sample of size 25. What is the t-value?
Finding the Critical t-Value
A random variable X follows a normal distribution with a mean of \(\mu = 5\) and a standard deviation of \(\sigma = 2\). What is the critical t-value for a 90% confidence interval?
Finding the z-Score
The average height of adults in a certain population is 170 cm with a standard deviation of 10 cm. If a person from this population has a height of 180 cm, what is the z-score?