Question

Q6) Allen Shoemaker derived a distribution of human body temperatures with a distinct mound shape. Suppose we assume that the temperatures of healthy humans are approximately normal with a mean of 37° Celsius and a standard deviation of 0.2 degrees.

(a) If 135 healthy people are selected at random, what is the probability that the average temperature for these people is 36.74°C or lower? (Round your answer to four decimal places.)

(b) Would you consider an average temperature of 36.74°C to be an unlikely occurrence, given that the true average temperature of healthy people is 37°C?

i) Since the probability is near 0.5, the average temperature of 36.74°C is likely.

ii) Since the probability is extremely large, the average temperature of 36.74°C is very likely.

iii) Since the probability is extremely small, the average temperature of 36.74°C is very unlikely.

iv) Since n is small, the average temperature of 36.74°C is unlikely. v) Since n is large, the average temperature of 36.74°C is likely.

Answer 1

-0.2 6 Ginen "=37 n=135 x= 36.74 we PCX 23674): - to find Probability 2-slove method Here : Z = x- 2- 36.74-37 0.2 18135 -3.02092701 . -3.0209 z = - 15.1046 And P( 436.74) = P(ZL-15.1046) from Standard Normal table- P(2<-15.1046) = 0 (PCX236.74) = 0 ② (ii) since the the rerage probability is extremely small, temperature of 36.746 is very unlikely