Answer:
a) 0.2588
b) 0.044015
c) 0.12609
Step-by-step explanation:
Using the TI-84 PLUS calculator
The formula for calculating a z-score is is z = (x-μ)/σ,
where x is the raw score
μ is the population mean
σ is the population standard deviation.
From the question, we know that:
μ = 119 inches
standard deviation σ = 17 inches
(a) What proportion of trees are more than 130 inches tall?
x = 130 inches
z = (130-119)/17
= 0.64706
Probabilty value from Z-Table:
P(x<130) = 0.7412
P(x>130) = 1 - P(x<130) = 0.2588
(b) What proportion of trees are less than 90 inches tall?
x = 90 inches
z = (90-119)/17
=-1.70588
Probability value from Z-Table:
P(x<90) = 0.044015
(c) What is the probability that a randomly chosen tree is between 95 and 105 inches tall?
For x = 95
z = (95-119)/17
= -1.41176
Probability value from Z-Table:
P(x = 95) = 0.07901
For x = 105
z = (105 -119)/17
=-0.82353
Probability value from Z-Table:
P(x<105) = 0.2051
The probability that a randomly chosen tree is between 95 and 105 inches tall
P(x = 105) - P(x = 95)
0.2051 - 0.07901
= 0.12609
