Instructor Katherine Cliff
Sketch the standard normal distribution.
A. Sketch a normal distribution with a bigger µ and the same standard deviation as the standard normal distribution. Label it a.
B. Sketch a normal distribution with a smaller σ and the same µ as the standard normal distribution. Label it b.
C. Sketch a normal distribution with a smaller µ and a bigger σ than the standard normal distribution. Label it c.
Example 1
What percent of the standard normal distribution is found in each region?
A. \(Z< -0.54\)
B. \(Z > 1.56\)
C. \(-2.1 < Z< 0.75\)
Example 2
At a state fair, passers-by are asked to guess the weight of Penelope the cow. The guesses are approximately normally distributed with a mean of 1200 pounds and a standard deviation of 10 pounds. What is the probability that a randomly selected person will guess that Penelope is more than 1225 pounds?
Example 2
At a state fair, passers-by are asked to guess the weight of Penelope the cow. The guesses are approximately normally distributed with a mean of 1200 pounds and a standard deviation of 10 pounds. What is the probability that a randomly selected person will guess that Penelope is more than 1225 pounds?
Example 3 For a standard normal distribution, find \(c\) such that \(P(z < c) = 0.9021\).
Example 4 Given a normal distribution with mean 20 and standard deviation 2, find \(x_1\) and \(x_2\) that contain the middle 90% of the distribution.
When sampling from a standard normal distribution, what is the probability that an observation falls in the specified region?
\[ Z<-0.3\]
\[P(Z < -0.24 \cup Z > 0.24)\]
The heights of adult men in America are normally distributed, with a mean of 69.8 inches and a standard deviation of 2.69 inches. The heights of adult women in America are also normally distributed, but with a mean of 64.4 inches and a standard deviation of 2.53 inches.
A. If a man is 6 feet 3 inches tall, what is his z-score (to four decimal places)?
The heights of adult men in America are normally distributed, with a mean of 69.8 inches and a standard deviation of 2.69 inches. The heights of adult women in America are also normally distributed, but with a mean of 64.4 inches and a standard deviation of 2.53 inches.
B. If a woman is 5 feet 11 inches tall, what is her z-score (to four decimal places)?
The heights of adult men in America are normally distributed, with a mean of 69.8 inches and a standard deviation of 2.69 inches. The heights of adult women in America are also normally distributed, but with a mean of 64.4 inches and a standard deviation of 2.53 inches.
C. Who is relatively taller?
A distribution of values is normal with a mean of 16.1 and a standard deviation of 64.7. Find the probability that a randomly selected value is between 50 and 106.7.
For a standard normal distribution, find c such that P(z > c) = 0.6948.
The mass of a species of mouse commonly found in houses is normally distributed with a mean of 20.5 grams with a standard deviation of 0.16 grams. Round your answers to 3 decimals.
A. 10% of all mice have a mass of less than how many grams?
The mass of a species of mouse commonly found in houses is normally distributed with a mean of 20.5 grams with a standard deviation of 0.16 grams. Round your answers to 3 decimals.
B. 30% of all mice have a mass of more than how many grams?
The mass of a species of mouse commonly found in houses is normally distributed with a mean of 20.5 grams with a standard deviation of 0.16 grams. Round your answers to 3 decimals.
C. Find \(x_1\) and \(x_2\) such that the middle 95% of mice will have a mass between \(x_1\) and \(x_2\) grams.