SOLUTION: Five hundred children participated in a field demonstration. Their heights averaged 110 cm with a standard deviation of 6 cm. a. What is the probability/percentage that a child

 

Hi,

Normal Distribution:

  μ  = 110   α = 6

Note: The -9999 is used as the smaller value to be at least 5 standard deviations from the mean.

 Using a TI calculator 0r similarly a Casio fx-115 ES plus <$20)

a. What is the probability/percentage that a child, picked at random has a height greater than 120 cm?

 P (x > 120 ) = 1 - P (x ≤ 120 )       | Continuous function

  P (x > 120 ) = 1 - normalcdf(-9999,120,110,6) = 1 - .9522 = .0478

b. What is the probability/percentage that the height of a child, picked at random, is less than 100 cm?

   P (x < 100 ) = P (x ≤ 100 )           |Continuous function

   P (x < 100 ) = P (x ≤ 100 ) =normalcdf(-9999,100,110,6) = .04778

c. Find the height such that 80% of the children are above it

    InvNorm( .8,6,110) = 115.0497

     height > 115cm for those above the 80th percentile

d. How many children belong to upper 40% of the group?

    invNorm( .6,6,110) = 111.5cm

     height > 111.5cm  for those to upper 40% of the group

Wish You the Best in your Studies.