The lengths of pregnancies are normally distributed with a mean of 269269 days and a standard deviation of 1515 days. a. Find th
e probability of a pregnancy lasting 309309 days or longer. b. If the length of pregnancy is in the lowest 44%, then the baby is premature. Find the length that separates premature babies from those who are not premature.
1 answer:
Answer:
a. 0.38%
b. 266.75 days
Step-by-step explanation:
We have the following data, mean (m) 269 and standard deviation (sd) 15, therefore:
a. The first thing is to calculate the number z:
z (x) = (x - m) / sd
z (309) = (309-269) / 15 = 2.67
When looking in the normal distribution table (attached), we have that at this value of z, the probability is:
P (z> 2.67), that is to say we must look in the table -2.67 and this value corresponds to 0.0038, that is to say 0.38%
b. Find the z-value with a left tail of 44%, i.e. 0.44. We look in the table for this value and what value of z corresponds.
invNorm (0.44) = -0.15
Find the corresponding number of days:
x = z * sd + m
we replace
d = -0.15 * 15 + 269 = 266.75 days
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The time for the village to dig the new well is about 7 1/2 years. At this time the population doubles from its current size.
<h3>How to graph a function?</h3>For a function f(x) = y, the steps to draw a graph for the given function are as follows:
- Consider certain values of x
- Substitute x values in the given function to obtain y values
- Plot the x and y values in the graph
- Join the points to know the variation.
It is given that,
f(x) = 200 ×
Village's population growing rate = 9.8%
Creating a table for x and f(x) values:
x: 0 2 4 6 8 10
f(x = 0) = f(0) = 200 × = 200
f(x = 2) = f(2) = 200 × = 241
f(x = 4) = f(4) = 200 × = 291
f(x = 6) = f(6) = 200 × = 350
f(x = 8) = f(8) = 200 × = 423
f(x = 10) = f(10) = 200 × = 509
So,
(x, f(x)): (0, 200) (2, 241) (4, 291) (6, 350) (8, 423) (10, 509)
Plotting these points in the graph and joining the points, the graph is shown below.
Finding the time for the village to dig a new well:
It is given that the population doubled from its current size, the village will need to dig new water well.
The current size of the village = 200
If it doubles for a certain time 't' = 400
So,
400 = 200 ×
⇒ = 2
⇒ log = log 2
⇒ t log(1.098) = 0.301
⇒ t × 0.04 = 0.301
∴ t = 7.525 years
Therefore, the village's population becomes double at the time 7 and half years from now. So, after 7 1/2 years, the village needs to dig a new well.
Learn more about the function and its graph here:
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