Answer:
P(-1 < z < 1) = 0.3174
Step-by-step explanation:
Mean (μ) = 1.62 ounces
Standard Deviation (σ) = 0.05
No of balls (sample size n) = 100
X = weight of a ball
Weight of a group of 100 balls must lie in the range 162 ± 0.5 ounces i.e. weight of a single ball will be 162/100 ± 0.5/100 ounces = 1.62 ± 0.005 ounces.
So, we need to find the probability P (1.615 < X < 1.625). We will use the central limit theorem.
z = (Χ' - μ)/(σ/
)
P (1.615 < X < 1.625) = (
< (Χ - μ)/(σ/) < 
)
= (-1 < z < 1)
We need to find the probability of P (-1 < z < 1) by looking at the Normal Distribution Probability Table.
In order to make our working simpler, we need to break P (-1 < z < 1) into two parts: P(z < 1) and P(z > -1)
The probability for areas under the normal curve are given for P(z>X) so we can directly find the probability of P (z > -1) by referring to the normal probability table.
P(z > -1) = 0.1587
We can calculate P(z < 1) by subtracting P(z >1) from the total probability (i.e. 1). P(z >1) can be obtained from the normal probability table.
P(z < 1) = 1 - 0.8413 = 0.1587
By adding the two probabilities together, we get:
P(-1 < z < 1) = P(z < 1) + P (z > -1)
= 0.1587 + 0.1587
P(-1 < z < 1) = 0.3174
The problem express that the fraction of time
worked by the three people need to be equivalent to one person working full
time. This means that the fraction need to add up to one. We know one person
works ½ time on the project and another works one third 1/3 time.
Given:
A = the amount of time that the third person needs
to work on the job to add up to one
1 = ½ +1/3 + A
1 – ½ - 1/3 = A
To subtract the fractions put them all over a
common denominator. Use 3 * 2 as the denominator.
1=6/6, ½ = 3/6, 1/3 = 2/6
A = 6/6 – 3/6 – 2/6
<span>A = 1/6 , The third person must work on the project</span>
Answer:
35, 67 and 78
Step-by-step explanation:
the angles are:
n, 2n-3 and 2n+8
there are 180 degrees in a triangle, so adding those terms together will give us 180
5n + 5 = 180
180 - 5 = 175
5n = 175
175 / 5 = 35
n = 35
now we have n we can put it in to the formula we have for the angles at the start:
n = 35
2n - 3 = 67
2n + 8 = 78
so the angles are
35, 67 and 78
The area of a circle A equals either:
πr² or πd²/4
96 = πd²/4 => d = 11 inches
The diameter of the second circle equals :
11*1.5 = 16.5 inches
The area equals: π(16.5)²/4 = 214 square inches
Good luck
Answer:
x = -7
Step-by-step explanation:
The whole line is 12
the whole line is also x + 14 and x + 12
so make them equal:
x+14 + x +12 = 12
2x + 26 = 12 now subtract 26 from both sides
2x = - 14 now divide both sides by 2
x = -7
