Question

Supposedly the distribution of the human's body temperature in the population has a mean of 37ºC and a standard deviation of 0.85ºC. If a sample of 105 people is chosen, calculate the following probabilities:

a) that the mean is less or equal to 36.9 ºC

b) that the mean is greater than 38.5 ºC

c) Find from what temperature the 10% of the hottest bodies are found

d) Find from what temperature the 5% of the coldest bodies are found

Answer 1

Solution :

Given that ,

mean = = 37

standard deviation = = 0.85

n = 105

= 37

= / n = 0.85 / 105  = 0.0830

P( 36.9 ) = P(( - ) / ( 36.9 - 37 ) / 0.0830)

= P(z -1.20 )

Using z table

= 0.1151

Probability = 0.1151

( b )

P( > 38.5 ) = 1 - P( < 38.5 )

= 1 - P[( - ) / < ( 38.5 - 37) / 0.0830 ]

= 1 - P(z < 18.07)

Using z table,    

= 1 - 1.0000

= 0.0000

Probability = 0.0000

( c )

The z - distribution of the 10% is

P(Z < z) =10% i

= P(Z < z ) = 0.10

= P(Z < -1.282 ) = 0.10

z = -1.282

Using z-score formula,

x = z * +

x = -1.282 * 0.0830 + 37

x = 36.8935

x = 36.89

( d )

The z - distribution of the 5% is

P(Z < z) = 5%

= P(Z < z ) = 0.05

= P(Z < -1.645 ) = 0.05

z = -1.645

Using z-score formula,

x = z * +

x = -1.645 * 0.0830 +37

x = 36.86