Assume that thermometer readings are normally distributed with a mean of 0degree
ID: 3153968 • Letter: A
Question
Assume that thermometer readings are normally distributed with a mean of 0degreeC and a standard deviation of 1.00degreeC. A thermometer is randomly selected and tested. In each case, draw a sketch, and find the temperature reading corresponding to the given information. 49. Find P_95, the 95th percentile. This is the temperature reading separating the bottom 95% from the top 5%. 50. Find P_1, the 1st percentile. This is the temperature reading separating the bottom 1% from the top 99%. 51. If 2.5% of the thermometers are rejected because they have readings that are too high and another 2.5% are rejected because they have readings that are too low, find the two readings that are cutoff values separating the rejected thermometers from the others. 52. If 0.5% of the thermometers are rejected because they have readings that are two low and another 0.5% are rejected because they have readings that are too high, find the two readings that are cutoff values separating the rejected thermometers from the others.Explanation / Answer
45.
z1 = lower z score = -1.96
z2 = upper z score = 1.96
Using table/technology, the left tailed areas between these z scores is
P(z < z1) = 0.024997895
P(z < z2) = 0.975002105
Thus, the area between them, by subtracting these areas, is
P(z1 < z < z2) = 0.95000421 [ANSWER]
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46.
Using a table/technology, the left tailed area of this is
P(z < 1.645 ) = 0.950015094 [ANSWER]
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47.
z1 = lower z score = -2.575
z2 = upper z score = 2.575
Using table/technology, the left tailed areas between these z scores is
P(z < z1) = 0.005012004
P(z < z2) = 0.994987996
Thus, the area between them, by subtracting these areas, is
P(z1 < z < z2) = 0.989975991 [ANSWER]
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48.
z1 = lower z score = -1.96
z2 = upper z score = 1.96
Using table/technology, the left tailed areas between these z scores is
P(z < z1) = 0.024997895
P(z < z2) = 0.975002105
Thus, the area between them, by subtracting these areas, is
P(z1 < z < z2) = 0.95000421
Thus, those outside this interval is the complement = 0.04999579 [ANSWER]
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