During the winter semester of 2021, the majority of classes were held online as opposed to in person. A professor decided to pre-record all of his lectures and make them all available so that students could access any of the videos at any time during the semester. Suppose the lengths of these pre-recorded lecture videos follow a normal distribution with a mean length of 57.28 minutes and a standard deviation of 8.887 minutes. Please use this information to answer the following questions and please use R (not the z-table) for any calculations. a. What is the probability that a randomly selected lecture video will be shorter than 55.8 minutes? Answer:________ Round to at least FOUR digits after the decimal if necessary.
During the winter semester of 2021, the majority of classes were held online as opposed to in person. A professor decided to pre-record all of his lectures and make them all available so that students could access any of the videos at any time during the semester. Suppose the lengths of these pre-recorded lecture videos follow a
a. What is the probability that a randomly selected lecture video will be shorter than 55.8 minutes?
Answer:________ Round to at least FOUR digits after the decimal if necessary.
b. The amount of time per lecture that the professor would have if the course had been offered 'in person' is 50 minutes. What is the probability that a randomly selected lecture video exceeds this allotted time?
Answer:________Round to at least FOUR digits after the decimal if necessary.
c. What is the minimum length (in minutes) that a recorded lecture video could be and still be in the longest 18% of videos?
Answer:________minutes. Round to at least FOUR digits after the decimal if necessary.
d. Suppose the z-score (standardized score) of a lecture video's length is given as 1.18. Which of the following statements is a correct interpretation of the meaning of this value?
A. The length of this video is 1.18 standard deviations longer than the average length
B. The length of this video is 1.18 minutes longer than the average length
C. The length of this video is 1.18 times longer than the average length
D. There is not enough information provided to interpret this value
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