The time taken for a computer to boot up, X, follows a normal distribution with

Question

The time taken for a computer to boot up, X, follows a normal distribution with mean 30 seconds and standard deviation 5 seconds.

1. What is th standardized score (z-score) for a boot up time of X= 30 seconds?

2. What is the standardized score (z-score) for a boot up time of x=20 seconds?

The average time tocomplete an exam, X, follows a normal probability distribution with mean = 60 minutes and standard deviation 30 minutes.

1. What is the probability that a randomly chosen student will complete the exam in 30 minutes or less?

2. By what time should 99% of the students have finished the exam? (i.e. what is the 99th percentile for X?)

Explanation / Answer

Z score formula is (x-mean)/std deviation. 1. 30-30/5= 0 2. 20-30/5= -2 1. Z score is 30-60/30= -1 Probability (from z table) is 0.1587 2. Factor for 99% from z table is 2.33 2.33= x-60/30 x= 129.9 minutes.

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