The accompanying data is on cube compressive strength (MPa) of concrete specimens. 112.4 97.0 92.7 86.0 102.0 99.3 95.8 103.5 89.0 86.7 A USE SALT (a) Is it plausible that the compressive strength for this type of concrete is normally distributed? O The normal probability plot is not acceptably linear, suggesting that a normal population distribution is not plausible. O The normal probability plot is not acceptably linear, suggesting that a normal population distribution is plausible. O The normal probability plot is acceptably linear, suggesting that a normal population distribution is not plausible. O The normal probability plot is acceptably linear, suggesting that a normal population distribution is plausible. (b) Suppose the concrete will be used for a particular application unless there is strong evidence that true average strength is less than 100 MPa. Should the concrete be used? Carry out a test of appropriate hypotheses. State the appropriate hypotheses. O Hot H= 100 H u> 100 O Hoi H= 100 HH 100 O Hoi H= 100 HH< 100 O Hoi H< 100 HiH = 100 O Hot H> 10 H H- 100 Calculate the test statistic and determine the P-value. (Round your test statistic to two decimal places and your P-value to four decimal places.) t- -1.37 Pvalue- o
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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