A model for normal human body temperature, X, when measured orally in °F, is that it is normally distributed, X ~ N(98.2,0.5184). (i) According to the model, what proportion of people have a normal body temperature of 99 °F or more? (ii) Find the normal body temperature such that, according to the model, only 10% of people have a lower normal body temperature. (iii) Let W denote normal human body temperature, when measured orally in °C. Given that W = (X - 32) and X ~ N (98.2,0.5184), what is the distribution of W?

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A model for normal human body temperature, X, when measured orally
in °F, is that it is normally distributed, X ~ N (98.2,0.5184).
(i) According to the model, what proportion of people have a normal
body temperature of 99 °F or more?
(ii) Find the normal body temperature such that, according to the
model, only 10% of people have a lower normal body temperature.
(iii) Let W denote normal human body temperature, when measured
orally in °C. Given that W = (X - 32) and X ~ N(98.2,0.5184),
what is the distribution of W?
(iv) According to the model that you just derived for W, what
proportion of people have a normal body temperature of between
36 °C and 36.8 °C?
Transcribed Image Text:A model for normal human body temperature, X, when measured orally in °F, is that it is normally distributed, X ~ N (98.2,0.5184). (i) According to the model, what proportion of people have a normal body temperature of 99 °F or more? (ii) Find the normal body temperature such that, according to the model, only 10% of people have a lower normal body temperature. (iii) Let W denote normal human body temperature, when measured orally in °C. Given that W = (X - 32) and X ~ N(98.2,0.5184), what is the distribution of W? (iv) According to the model that you just derived for W, what proportion of people have a normal body temperature of between 36 °C and 36.8 °C?
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