Question

The body temperatures of all mosquitoes in a county have a mean of 57∘F and a standard deviation of 10∘F. What is the probability that in a sample of 25 mosquitoes the mean body temperature is greater than 59∘F, assuming the underlying distribution is normal? Do not write probability in terms of percentage. Round your answer to two decimal places.

Answer 1

Solution :

Given that ,

mean = = 57

standard deviation = = 10

n = 25

= 57 and

= / n = 10 / 25 = 2

P( > 59) = 1 - P( < 59)

= 1 - P(( - ) / < (59 - 57) / 2)

= 1 - P(z < 1)

= 1 -0.8413

= 0.1587 = 0.16

Probability = 0.16