Suppose that 14 children, who were learning to ride two-wheel bikes, were surveyed to determine how long they had to use training wheels. It was revealed that they used them an average of eleven months with a sample standard deviation of two months. Assume that the underlying population distribution is normal.
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!
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Part (a)
(i) Enter an exact number as an integer, fraction, or decimal.
x =
(ii) Enter an exact number as an integer, fraction, or decimal.
sx =
(iii) Enter an exact number as an integer, fraction, or decimal.
n =
(iv) Enter an exact number as an integer, fraction, or decimal.
n − 1 = -
Part (b)
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Part (c)
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Part (d)
Which distribution should you use for this problem? (Enter your answer in the form z or tdf where df is the degrees of freedom.)
Explain your choice.Construct a 99% confidence interval for the population mean length of time using training wheels.(i) State the confidence interval. (Round your answers to two decimal places.)
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(ii) Sketch the graph. (Round your answers to two decimal places. Enter your ?/2 to three decimal places.)(iii) Calculate the error bound. (Round your answer to two decimal places.)CL =
=? 2
=? 2
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