Answer:
A) 68.33%
B) (234, 298)
Step-by-step explanation:
We have that the mean is 266 days (m) and the standard deviation is 16 days (sd), so we are asked:
A. P (250 x < 282)
P ((x1 - m) / sd < x < (x2 - m) / sd)
P ((250 - 266) / 16 < x < (282 - 266) / 16)
P (- 1 < z < 1)
P (z < 1) - P (-1 < z)
If we look in the normal distribution table we have to:
P (-1 < z) = 0.1587
P (z < 1) = 0.8413
replacing
0.8413 - 0.1587 = 0.6833
The percentage of pregnancies last between 250 and 282 days is 68.33%
B. We apply the experimental formula of 68-95-99.7
For middle 95% it is:
(m - 2 * sd, m + 2 * sd)
Thus,
m - 2 * sd <x <m + 2 * sd
we replace
266 - 2 * 16 <x <266 + 2 * 16
234 <x <298
That is, the interval would be (234, 298)
Answer:
Provided that the sample size, n, is sufficiently large (greater than 30), the distribution of sample means selected from a population will have a normal distribution, according to the Central Limit Theorem.
Explanation:
1. As n increases, the sample mean approaches the population mean
(The Law of Large numbers)
2. The standard error of the sample is
σ/√n
where σ = population standard deviation.
As n increases, the standard error decreases, which means that the error
between the sample and population means decreases.
The answer to this would be 6
Answer: 6) x= 17 Same side interior angles sum to 180.
7) x= 3 Alternate exterior angles are equal.
8) x= 35 Corresponding angles are equal.
9) x= 12 Alternate interior angles are equal
Step-by-step explanation:
6) x= Same side interior angles sum to 180.
53+(8x-9)= 180
44+8x= 180
Subtract 44 from both sides
8x= 136
Divide both sides by 8
X = 17
7) x= Alternate exterior angles are equal. 15x+29= 26x-4
Subtract 15x from both sides
29= 11x-4
Add 4 to both sides
33= 11x
Divide both sides by 11
X=3
8) x= Corresponding angles are equal.
4x+7= 6x-63
Subtract 4x from both sides
7 = 2x -63
Add 63 to both sides
70= 2x
Divide both sides by 2
X= 35
9) x= Alternate interior angles are equal
9x+37= 14x-23
Subtract 9 x from both sides
37= 5x -23
Add 23 to both sides
60= 5x
Divide both sides by 5
12=x
Answer:
Below.
Step-by-step explanation:
a) A = {1, 2, 5, 10}
b) B = {1, 3, 5, 15}
c) A∩B = {1, 5} ( elements common to A and B).
d) A∪B = {1, 2, 3, 5, 10, 15} (total elements in A and B).
