Question

if we take a sample of 10 infants, what is the probability that their mean weight(weight is normally distributed in the population) will be above the 61st population percentile for weight?Give your answer as a probability and round to TWO decimal places.

Answer 1

Here sample size = 10

Here let say their mean weight is

so here let say the mean of the population is and standard deviation is

so for 61 percentile, z value is NORMSINV(0.61) = 0.2793

so here we have to find the probability

P( > + 0.2793 )

Here for ~ Normal (; /sqrt(10))

so here

Z value = ( + 0.2793 - )/ (/sqrt(10)) = 0.8833

so here

P( > + 0.2793 ) = 1 - P(Z < 0.8833) = 1 - NORMSDIST(0.8833) = 1- 0.8115 = 0.1885