Math 110 Chapter 7, 8, 9 solutions Correct and accurate.

Math 110 Chapter 7, 8, 9 solutions
Correct and accurate.
Math 110 Chapter 7, 8, 9 solutions
Correct and accurate.
Probability Density Curve - ANSWER the curve used to describe the distribution of a continuous random
variable



Normal Curve - ANSWER the bell-shaped curve that describes the distribution of many physical and
psychological attributes. Most scores fall near the average, and fewer and fewer scores lie near the
extremes



Z-Score - ANSWER a measure of how many standard deviations you are away from the norm (average or
mean)



Example: A woman whose height is x=67 inches from a normal population with mean μ=64 and σ=3
inches.



What is the Z-score? - ANSWER The Z-score is z = (x - μ)/σ = (67-64)/3 = 1



z score formula - ANSWER z = (x - μ)/σ



finding the area under the normal curve - ANSWER normalcdf(lower, upper, μ, σ)



To get it: 2nd+Var -> 2: norm



Example: Find the area to the left of z = 1.26 in a normal curve - ANSWER normalcdf(-1E99, 1.26, 0, 1)



Example: A study reported that the length of pregnancy from conception to birth is approximately
normally distributed with mean μ = 272 days and standard deviation σ = 9 days. What proportion of
pregnancies last less than 259 days? - ANSWER Step 1: Find the Z-Score. (259-272)/9 = -1.444

,Math 110 Chapter 7, 8, 9 solutions
Correct and accurate.

Step 2: Use the Z-Score to find area left of Z = -1.444



normalcdf(-1E99, -1.444, 0, 1)



Finding X from z-score - ANSWER invNorm(Area to the left, μ, σ)



To get to it: 2nd+Vars -> 3:invNorm



Mensa is an organization whose members possess IQs in the top 2% of the population. If the IQs are
normally distributed with a mean of 100 and a standard deviation of 15, what is the minimum IQ
necessary for admission? - ANSWER First: Find the z-score that corresponds to the given area using
invNorm.



z = invNorm(0.98, 0, 1)



x = μ + z * σ = 100 + 2.0537(15)



x = 130.8



x ≈ 131



mean of sampling distribution of x̄ - ANSWER μx̄ = μ



The mean of the sampling distribution is denoted by μx̄ and is equal to the mean of the population μ.



standard deviation of sampling distribution of x̄ - ANSWER σx̄ = σ/√n

, Math 110 Chapter 7, 8, 9 solutions
Correct and accurate.
The standard deviation of the sampling distribution (Standard Error) is denoted by σx̄ and equals the
standard deviation of the population divided by the square root of the sample size.



Sampling distribution of a skewed population - ANSWER if a population is skewed, a larger sample size is
necessary for the sampling distribution of x̄ to be approximately normal.



The Central Limit Theorem - ANSWER The theory that, as sample size increases, the distribution of
sample means of size n, randomly selected, approaches a normal distribution.



In practice, a sample size of n>30 is enough.



Example: Based on data from the U.S. Census, the mean age of college students in 2011 was μ = 25
years, with a standard deviation of σ = 9.5 years. A simple random sample of 125 students is drawn.
What is the probability that the sample mean age of the students is greater than 26 years? - ANSWER
Step 1: Confirm the assumptions.

n=135>30

Thus, we may use the normal curve.



Step 2: Then, compute μx̄ and σx̄.



μx̄ = μ = 25

σx̄ = 9.5/√125 = 0.85



normalcdf(lower, upper, μx̄, σx̄)

normalcdf(26, 1E99, 25, 0.85) = 0.1197



Mean of a sampling distribution of p̂ - ANSWER μp̂ = p̂



The mean of the sampling distribution of p̂ is equal to the population proportion