The average amount of money spent for lunch per person in the college cafeteria is $7.41 and the standard deviation is $2.2. Suppose that 16 randomly selected lunch patrons are observed. Assume the distribution of money spent is normal, and round all answers to 4 decimal places where possible. For the group of 16 patrons, find the probability that the average lunch cost is between $7.515 and $8.22. For part d), is the assumption that the distribution is normal necessary? No or Yes
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!
The average amount of money spent for lunch per person in the college cafeteria is $7.41 and the standard deviation is $2.2. Suppose that 16 randomly selected lunch patrons are observed. Assume the distribution of money spent is normal, and round all answers to 4 decimal places where possible.
- For the group of 16 patrons, find the
probability that the average lunch cost is between $7.515 and $8.22. - For part d), is the assumption that the distribution is normal necessary? No or Yes
1.
Let denotes the
The probability that the average lunch cost is between $7.515 and $8.22 is,
The probability of z less than 1.4727 can be obtained using the excel formula “=NORM.S.DIST(1.4727,TRUE)”. The probability value is 0.9296.
The probability of z less than 0.1909 can be obtained using the excel formula “=NORM.S.DIST(0.1909,TRUE)”. The probability value is 0.5757.
The required probability value is,
Thus, the probability that the average lunch cost is between $7.515 and $8.22 is 0.3539.
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