Question 18 The z-scores of the test results of a sample of 43 students follow the T-distribution with 42 degrees of freedom. Let X be the z-score of a randomly selected student. 1. Describe the distribution of X: P(X<-1.7)=0.05 X<0 P(X<2) P(X<-1.7)=0.05 X<0 P(X<2) 2. Use the random variable notation to express symbolically each of the following: P(X<-1.7)=0.05 X<0 P(X<2) ii. more than 2: ✓ The probability of an event in which the z-score of a randomly selected student is less than -1.7 is equal to 0.05. X-? ✔ ? ✓An event in which the z-score of a randomly selected student is less than 0. iii. between -1 and 0.7: LNBT iv. more than 9.6: T U N ✓ The probability of an event in which the z-score of a randomly selected student is less than 2. 3. Use technology to find the probability that the z-score of a randomly selected student is: i. less than 0: v. less than 12.3: (df= 4. Find the 2-th percentile: X 2% (round the answer to 2 decimal places) (round the answer to 2 decimal places) (round the answer to 2 decimal places) (round the answer to 2 decimal places) (round the answer to 2 decimal places) (round the answer to 2 decimal places)

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● Question 18
The z-scores of the test results of a sample of 43 students follow the T-distribution with 42 degrees of
freedom. Let X be the z-score of a randomly selected student.
1. Describe the distribution of X:
P(X<-1.7)=0.05
X<0
P(X<2)
U
N
2. Use the random variable notation to express symbolically each of the following:
P(X<-1.7)=0.05
|X<0
P(X<2)
P(X<-1.7)=0.05
X<0
P(X<2)
✓ The probability of an event in which the z-score of a randomly selected
student is less than -1.7 is equal to 0.05.
✓An event in which the z-score of a randomly selected student is less than 0.
✓ The probability of an event in which the z-score of a randomly selected
student is less than 2.
ii. more than 2:
X-? (df=
3. Use technology to find the probability that the z-score of a randomly selected student is:
i. less than 0:
iii. between -1 and 0.7:
Z
iv. more than 9.6:
v. less than 12.3:
4. Find the 2-th percentile:
I 2%
(round the answer to 2 decimal places)
(round the answer to 2 decimal places)
(round the answer to 2 decimal places)
(round the answer to 2 decimal places)
(round the answer to 2 decimal places)
(round the answer to 2 decimal places)
Transcribed Image Text:● Question 18 The z-scores of the test results of a sample of 43 students follow the T-distribution with 42 degrees of freedom. Let X be the z-score of a randomly selected student. 1. Describe the distribution of X: P(X<-1.7)=0.05 X<0 P(X<2) U N 2. Use the random variable notation to express symbolically each of the following: P(X<-1.7)=0.05 |X<0 P(X<2) P(X<-1.7)=0.05 X<0 P(X<2) ✓ The probability of an event in which the z-score of a randomly selected student is less than -1.7 is equal to 0.05. ✓An event in which the z-score of a randomly selected student is less than 0. ✓ The probability of an event in which the z-score of a randomly selected student is less than 2. ii. more than 2: X-? (df= 3. Use technology to find the probability that the z-score of a randomly selected student is: i. less than 0: iii. between -1 and 0.7: Z iv. more than 9.6: v. less than 12.3: 4. Find the 2-th percentile: I 2% (round the answer to 2 decimal places) (round the answer to 2 decimal places) (round the answer to 2 decimal places) (round the answer to 2 decimal places) (round the answer to 2 decimal places) (round the answer to 2 decimal places)
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