Question One A university teaching room has a capacity to hold 50 students The probability that any one student attends the teaching room during class is 0 7 If 50 students are enrolled in the class, calculate the probability that Exactly 40 attend the class Fewer than 30 attend the class Between 30 and 40 (inclusive) attend the class (Check 0 912) More than 10 students do not attend the class Based on the information calculate The Expected Value for the number of students who attend the class The Variance and Standard Deviation of the number of students who attend the class If the university enrolled 60 students in the class, what is the probability that the classroom is not full on any one day (Check 0 986) Question Two A manufacturing process produces tyres with a lifetime that is normally distributed with a mean of 60,000km and a standard deviation of 10,000km Using both the standard normal formula and tables, and using excel to check, calculate the following (including a picture of the area under the curve for a to c ) The probability that any one tyre lasts longer than 75,000km The probability that any one tyre lasts between 45,000 and 65,000km The probability that any one tyre lasts less than 72,500km The lifespan of the bottom 15 of tyres If two tyres are selected at random so that they would be considered independent of each other, what is the probability that both last longer than 50,000km (check 0 708)

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Question One A university teaching room has a capacity to hold 50 students. The probability that any one student attends the teaching room during class

Question One

A university teaching room has a capacity to hold 50 students. The probability that any one student attends the teaching room during class is 0.7. If 50 students are enrolled in the class, calculate the probability that:

Exactly 40 attend the class
Fewer than 30 attend the class
Between 30 and 40 (inclusive) attend the class (Check: 0.912)
More than 10 students do not attend the class

Based on the information calculate:

The Expected Value for the number of students who attend the class.
The Variance and Standard Deviation of the number of students who attend the class.
If the university enrolled 60 students in the class, what is the probability that the classroom is not full on any one day. (Check: 0.986)

Question Two

A manufacturing process produces tyres with a lifetime that is normally distributed with a mean of 60,000km and a standard deviation of 10,000km. Using both the standard normal formula and tables, and using excel to check, calculate the following (including a picture of the area under the curve for a. to c.)

The probability that any one tyre lasts longer than 75,000km.
The probability that any one tyre lasts between 45,000 and 65,000km.
The probability that any one tyre lasts less than 72,500km.
The lifespan of the bottom 15% of tyres?
If two tyres are selected at random so that they would be considered independent of each other, what is the probability that both last longer than 50,000km. (check: 0.708)