Answer:
15.85%
Explanations:
According to the empirical rule for normal probability;
• 68% of given, data falls within 1σ of the mean
,
• 95%, of the given data falls within 2σ of the mean
,
• 99.7% of all data falls within 3σ of the mean
This rule shows an even distribution among the mean
From the data, we can say that 34% of the data is within μ±1σ
Given the following data
Mean = 194 pages
Standard deviation = 25
Hence 1 standard deviation of the mean will be 194 - 25 = 169 showing that 34% of data fall in that range
Since we need the probability that a randomly selected book has fewer than 169 pages, we use the normal distribution property which states:
50% of the data is left of the mean of which 34% fall within 1 standard deviation, hence the remaining would fall fewer than 169.
Pr(a randomly selected book has fewer than 169 pages) = 50% - 34% = 16%
To determine the final probability, we will subtract the half of 0.3(100-99.7) to have:
Pr(a randomly selected book has fewer than 169 pages) = 16 - 0.3/2
Pr(a randomly selected book has fewer than 169 pages) = 16 - 0.15
Pr(a randomly selected book has fewer than 169 pages) = 15.85%