The probability that the thermometer reading is between 99.7 and 100.3 deg c is 0.84.
The probability that the thermometer reading is between 99.7 and 100.3 deg c is 0.84. This can be calculated using the cumulative distribution function (CDF) of the normal distribution, which is given by:
P(X <= x) = (1/sqrt(2*pi*sigma^2))*integral(-infinity to x of e^(-((x-mu)^2)/(2*sigma^2))dx
For the given parameters, the CDF is:
P(X <= x) = (1/sqrt(2*pi*0.1^2))*integral(-infinity to x of e^(-((x-99.8)^2)/(2*0.1^2))dx
For the interval 99.7 to 100.3, the probability is the difference between the CDF values of the two endpoints:
P(99.7 <= X <= 100.3) = P(X <= 100.3) - P(X <= 99.7)
= 0.84
The probability that the thermometer reading is between 99.7 and 100.3 deg c is 0.84. This can be calculated by finding the cumulative distribution function (CDF) of the normal distribution for the given parameters of mean 99.8 deg c and standard deviation of 0.1 deg c, and then taking the difference between the CDF values of the two endpoints of 99.7 and 100.3.
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