1. Suppose that the average internet download speed for AT&T is 1.33 Mbps with a standard deviation of 1.13 Mbps. (Note: I know that these are very poor internet download speeds, but this was Ms. Sutter's reality before she switched internet companies.) a) Find the probability that, in a sample of 45 AT&T customers, the average internet download speed is no more than 2 Mbps. b) Find the probability that, in a sample of 20 AT&T customers, the average internet download speed is less than 1.6 Mbps. c) Find the probability that an AT&T customer has an internet download speed of more than 2.4 Mbps. Assume that the data is normally distributed.
Continuous Probability Distributions
Probability distributions are of two types, which are continuous probability distributions and discrete probability distributions. A continuous probability distribution contains an infinite number of values. For example, if time is infinite: you could count from 0 to a trillion seconds, billion seconds, so on indefinitely. A discrete probability distribution consists of only a countable set of possible values.
Normal Distribution
Suppose we had to design a bathroom weighing scale, how would we decide what should be the range of the weighing machine? Would we take the highest recorded human weight in history and use that as the upper limit for our weighing scale? This may not be a great idea as the sensitivity of the scale would get reduced if the range is too large. At the same time, if we keep the upper limit too low, it may not be usable for a large percentage of the population!
![Please remember to prove normality for every problem!!
1. Suppose that the average internet download speed for AT&T is 1.33 Mbps with a standard
deviation of 1.13 Mbps. (Note: I know that these are very poor internet download speeds, but this
was Ms. Sutter's reality before she switched internet companies.)
a) Find the probability that, in a sample of 45 AT&T customers, the average internet download
speed is no more than 2 Mbps.
b) Find the probability that, in a sample of 20 AT&T customers, the average internet download
speed is less than 1.6 Mbps.
c) Find the probability that an AT&T customer has an internet download speed of more than 2.4
Mbps. Assume that the data is normally distributed.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F3e5b31ba-0441-40a7-ac0a-56d5bae166d9%2F9d9f9db9-af74-41fe-81a3-838a0abdbd1d%2Fqkvza9_processed.jpeg&w=3840&q=75)
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