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Redeyestudio53
12.10.2020 •
Mathematics
Baby weights: The weight of male babies less than 2 months old in the United States is normally distributed with mean 11.8 pounds and standard deviation 3.1 pounds. Use the TI-84 Plus calculator to answer the following. (a) What proportion of babies weigh more than 13 pounds? (b) What proportion of babies weigh less than 14 pounds? (c) What proportion of babies weigh between 11 and 15.8 pounds? (d) Is it unusual for a baby to weigh more than 18 pounds? Round the answers to four decimal places.
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Ответ:
(a)0.3493
(b) 0.7611
(c) 0.5034
(d) No it is not unusual
Step-by-step explanation:
Using the TI-84 Plus calculator to answer the following
The formula for calculating a z-score is is z = (x-μ)/σ, where x is the raw score, μ is the population mean, and σ is the population standard deviation.
Mean 11.8 pounds and Standard deviation 3.1 pounds.
(a) What proportion of babies weigh more than 13 pounds?
z = (x-μ)/σ
= 13 - 11.8/3.1
= 0.3871
Probability value from Z-Table:
P(x<13) = 0.65066
P(x>13) = 1 - P(x<13) = 0.34934
The proportion of babies weigh more than 13 pounds is 0.3493
(b) What proportion of babies weigh less than 14 pounds?
z = (x-μ)/σ
= 14 - 11.8/3.1
= 0.70968
Probability value from Z-Table:
P(x<14) = 0.76105
The proportion of babies weigh less than 14 pounds is 0.7611
(c) What proportion of babies weigh between 11 and 15.8 pounds?
For x = 11
z = (x-μ)/σ
= 11 - 11.8/3.1
= -0.25806
Probability value from Z-Table:
P(x = 11) = 0.39818
For x = 15.8
z = (x-μ)/σ
= 15.8 - 11.8/3.1
= 1.29032
Probability value from Z-Table:
P(x = 15.8) = 0.90153
The proportion of babies weigh between 11 and 15.8 pounds
P(x = 15.8) - P(x = 11)
= 0.90153 - 0.39818
= 0.50335
≈ 4 decimal places = 0.5034
(d) Is it unusual for a baby to weigh more than 18 pounds?
z = (x-μ)/σ
= 18 - 11.8/3.1
= 2
Probability value from Z-Table:
P(x≤ 18) = P(x = 18) =
0.97725
No it is not unusual to have a Weight of 18 pounds
Round the answers to four decimal places.
Ответ:
Step-by-step explanation:
Hi there!
We're given
, and that
is a translation of
6 units up.
This means that
.
Rewrite the equation
This would be our final equation. It does not look like the form
, However, when rewritten as
, we can tell clearly that it is.
I hope this helps!