Suppose you are a marine biologist studying a particular species of whales. The average length of this whale species is 60 feet and the standard deviation is 12 feet. The average length of whales in Normally distributed. 15. You find one member of this particular species of whales and measure it to find its length is 48 feet. What is the z-score corresponding to the length of this whale? a) 2 b) -2 c) -1.0 d) 1.0 16. What is the probability you find a whale smaller than the one referred to in the previous question? a) .8413 b).1587 c) 4801 d) - 4801 17. You find old research on this species of whales that only reports the z-scores of lengths and not the actual lengths of whales. One particular whale stands out to you because it has a z-score of 5.2. What does the z-score tell you? a) This whales is much larger than the mean. b) This whale is much smaller than the mean c) The whale is an average length d) Not enough information is given. 18. Which of the following is a true statement? (Assume that the first quartile and minimum for this data set are not equal.) a) the IQR is always bigger than the range for a given data set. b) the IQR is always smaller than the range. c) the IQR is equal to the range. d) this cannot be determined from the given information. 19. Which of the following is not true about normal curves? a) They all have mean 0. b) They are all symmetric. c) The area underneath the curve is equal to 1. d) They are all bell shaped. 20. What is the biggest advantage of the standard deviation over the variance? a) The standard deviation is always smaller than the variance. b) The standard deviation is calculated with the median instead of the mean. c) The standard deviation is better for describing skewed distributions.
Suppose you are a marine biologist studying a particular species of whales. The average length of this whale species is 60 feet and the standard deviation is 12 feet. The average length of whales in Normally distributed. 15. You find one member of this particular species of whales and measure it to find its length is 48 feet. What is the z-score corresponding to the length of this whale? a) 2 b) -2 c) -1.0 d) 1.0 16. What is the probability you find a whale smaller than the one referred to in the previous question? a) .8413 b).1587 c) 4801 d) - 4801 17. You find old research on this species of whales that only reports the z-scores of lengths and not the actual lengths of whales. One particular whale stands out to you because it has a z-score of 5.2. What does the z-score tell you? a) This whales is much larger than the mean. b) This whale is much smaller than the mean c) The whale is an average length d) Not enough information is given. 18. Which of the following is a true statement? (Assume that the first quartile and minimum for this data set are not equal.) a) the IQR is always bigger than the range for a given data set. b) the IQR is always smaller than the range. c) the IQR is equal to the range. d) this cannot be determined from the given information. 19. Which of the following is not true about normal curves? a) They all have mean 0. b) They are all symmetric. c) The area underneath the curve is equal to 1. d) They are all bell shaped. 20. What is the biggest advantage of the standard deviation over the variance? a) The standard deviation is always smaller than the variance. b) The standard deviation is calculated with the median instead of the mean. c) The standard deviation is better for describing skewed distributions.
Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018
18th Edition
ISBN:9780079039897
Author:Carter
Publisher:Carter
Chapter10: Statistics
Section10.4: Distributions Of Data
Problem 19PFA
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Inverse Normal Distribution
The method used for finding the corresponding z-critical value in a normal distribution using the known probability is said to be an inverse normal distribution. The inverse normal distribution is a continuous probability distribution with a family of two parameters.
Mean, Median, Mode
It is a descriptive summary of a data set. It can be defined by using some of the measures. The central tendencies do not provide information regarding individual data from the dataset. However, they give a summary of the data set. The central tendency or measure of central tendency is a central or typical value for a probability distribution.
Z-Scores
A z-score is a unit of measurement used in statistics to describe the position of a raw score in terms of its distance from the mean, measured with reference to standard deviation from the mean. Z-scores are useful in statistics because they allow comparison between two scores that belong to different normal distributions.
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Transcribed Image Text:Suppose you are a marine biologist studying a particular species of whales. The average
length of this whale species is 60 feet and the standard deviation is 12 feet. The average
length of whales in Normally distributed.
15. You find one member of this particular species of whales and measure it to find its
length is 48 feet. What is the z-score corresponding to the length of this whale?
a) 2
b) -2
c) -1.0
d) 1.0
16. What is the probability you find a whale smaller than the one referred to in the
previous question?
a) .8413
b).1587
c) 4801
d) - 4801
17. You find old research on this species of whales that only reports the z-scores of
lengths and not the actual lengths of whales. One particular whale stands out to you
because it has a z-score of 5.2. What does the z-score tell you?
a) This whales is much larger than the mean.
b) This whale is much smaller than the mean
c) The whale is an average length
d) Not enough information is given.
18. Which of the following is a true statement? (Assume that the first quartile and
minimum for this data set are not equal.)
a) the IQR is always bigger than the range for a given data set.
b) the IQR is always smaller than the range.
c) the IQR is equal to the range.
d) this cannot be determined from the given information.
19. Which of the following is not true about normal curves?
a) They all have mean 0.
b) They are all symmetric.
c) The area underneath the curve is equal to 1.
d) They are all bell shaped.
20. What is the biggest advantage of the standard deviation over the variance?
a) The standard deviation is always smaller than the variance.
b) The standard deviation is calculated with the median instead of the mean.
c) The standard deviation is better for describing skewed distributions.
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