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Giabear23
12.10.2020 •
Mathematics
ree heights: Cherry trees in a certain orchard have heights that are normally distributed with mean μ = 119 inches and standard deviation σ = 17 inches. Use the TI-84 PLUS calculator to answer the following. Round the answers to at least four decimal places. (a) What proportion of trees are more than 130 inches tall? (b) What proportion of trees are less than 90 inches tall? (c) What is the probability that a randomly chosen tree is between 95 and 105 inches tall? Part: 0 / 30 of 3 Parts Complete Part 1 of 3 What proportion of trees are more than 130 inches tall? The proportion of trees that are more than 130 inches tall is .
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Ответ:
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
Ответ:
-4 1/2, -1.6, 2 5/8, 6.8. That is the order from least to greatest.