Question

statistics - chapter one and two make-up test - fall 2023 3 0 for questions 1-9, describe what each term means in statistics. do not recite formal definitions, rather explain what it means as if to someone who is new to the class. cite examples if you like. 1. population 2. sample 3. designed experiment 4. skewed right graph 5. why are samples often used in statistical surveys instead of a census? 6. if a sample is used, why is it so important that it be
epresentative\? 7. is it possible for 50% of the numbers in a data set to be \above average\? explain. 8. describe the weaknesses/strengths of the mean and median. 9. describe what an outlier of a data set is. a certain test has mean score of 50 (x = 40) and standard deviation of 5 (s = 5) with a normal distribution. find: (use normalcdf) 10. the percent of people scoring between 47 and 53. 11. the percent of people scoring between 40 and 50. 12. the percent of people scoring below 55. 13. the percentile rank for a score of 60. 14. the percentile rank for a score of 44. 15. the z-score for a score of 63 (i.e. x = 63) 16. the score that corresponds to a z-value of -2.2.

Explanation:

Question 10:

Step1: Recall normalcdf parameters

The normalcdf function in statistics for a normal distribution takes the form normalcdf(lower, upper, mean, standard deviation). Here, lower = 47, upper = 53, mean ($\mu$) = 50, standard deviation ($\sigma$) = 5.

Step2: Apply normalcdf

Using the formula normalcdf(47, 53, 50, 5). We can also standardize the values using z - scores. The z - score formula is $z=\frac{x-\mu}{\sigma}$. For $x = 47$, $z_1=\frac{47 - 50}{5}=\frac{- 3}{5}=-0.6$. For $x = 53$, $z_2=\frac{53 - 50}{5}=\frac{3}{5}=0.6$. Then we find the area between $z=-0.6$ and $z = 0.6$ using the standard normal table or a calculator. The area between $z=-0.6$ and $z = 0.6$ is the same as $P(-0.6

Step1: Identify normalcdf parameters

For normalcdf, lower = 40, upper = 50, mean ($\mu$) = 50, standard deviation ($\sigma$) = 5.

Step2: Apply normalcdf or use z - scores

Using z - scores: For $x = 40$, $z=\frac{40 - 50}{5}=\frac{-10}{5}=-2$. For $x = 50$, $z=\frac{50 - 50}{5}=0$. We need to find $P(-2

Step1: Determine normalcdf parameters

For normalcdf, lower = -∞ (we can use a very small number like -1000), upper = 55, mean ($\mu$) = 50, standard deviation ($\sigma$) = 5.

Step2: Apply normalcdf or use z - scores

Using z - scores: For $x = 55$, $z=\frac{55 - 50}{5}=\frac{5}{5}=1$. We need to find $P(Z < 1)$. From the standard normal table, $P(Z < 1)=0.8413$. So the area to the left of 55 (percent of people scoring below 55) is 0.8413 or 84.13%.

Answer:

The percent of people scoring between 47 and 53 is approximately 45.14%.

Question 11: