This question is incomplete, the complete question is;
A sample of size 86 will be drawn from a population with mean 90 and standard deviation 24. Use the TI-84 calculator Part 1 of 2
Find the probability that x will be more than 89. Round the answer to at least four decimal places. The probability that will be more than 89 is Part 2 of 2 Find the 60 percentile of x. Round the answer to two decimal places. The 60 percentile is
.
Answer:
part 1) the probability that x will be more than 89 is 0.6517
part 2) the 60 percentile of x is 90.65
Step-by-step explanation:
Given that;
u = 90, α = 24, n = 86
Part 1 says Find the probability that x will be more than 89
p ( x > 89 ) = p (( x - u)/α√n > (89-90)/24/√86 ))
= p ( z > - 0.39 ) = 1 - p (z ≤ - 0.39 )
from z table, 0.39 → 0.3483
= 1 - 0.3483 = 0.6517
∴ the probability that x will be more than 89 is 0.6517
part 2 says Find the 60 percentile of x
p( Z < z ) = 0.60
now from the z-table, p(Z < 0.25 ) = 0.60
and we that x = u + z(α/√n)
x = 90 + 0.25( 24 / √ 86
x = 90.64699 ≈ 90.65
∴ the 60 percentile of x is 90.65
