Answer:
Step-by-step explanation:
Let us assume that the length of fishes in the tank is normally distributed. Thus, x is the random variable representing the length of fishes in the tank. Since the population mean and population standard deviation are known, we would apply the formula,
z = (x - µ)/(σ/√n)
Where
x = sample mean
µ = population mean
σ = standard deviation
number of samples
From the information given,
µ = 15
σ = 4
n = 31
We want to find the probability that x is between (15 - 0.5) inches and (15 + 0.5) inches. The probability is expressed as
P(14.5 ≤ x ≤ 15.5)
For x = 14.5
z = (14.5 - 15)/(4/√31) = - 0.7
Looking at the normal distribution table, the probability corresponding to the z score is 0.2420
For x = 15.5
z = (15.5 - 15)/(4/√31) = 0.7
Looking at the normal distribution table, the probability corresponding to the z score is 0.7580
Therefore,
P(14.5 ≤ x ≤ 15.5) = 0.7580 - 0.2420 = 0.5160
Answer:
see explanation
Step-by-step explanation:
the equation of a circle centred at the origin is
x² + y² = r² ( r is the radius )
(11)
- 81 + x² = - y² ( add y² to both sides )
- 81 + x² + y² = 0 ( add 81 to both sides )
x² + y² = 81 ← in standard form
with centre = (0, 0 ) and r = 
= 9
(12)
y² + x² - 196 = 0 ( add 196 to both sides )
x² + y² = 196 ← in standard form
with centre = (0, 0 ) and r = 
= 14
Answer:
y=-2x-3
Step-by-step explanation:
m=(y2-y1)/(x2-x1)
m=(-5-(-3))/(1-0)
m=(-5+3)/1
m=-2/1
m=-2
y-y1=m(x-x1)
y-(-3)=-2(x-0)
y+3=-2(x)
y+3=-2x
y=-2x-3
I believe that in this problem, we are asked for the hypotenuse of the triangle that can be formed when we make a right triangle out of the planes and the intersection of their paths. To solve for the hypotenuse of a right triangle, we make use of the equation,
h² = 64.2² + 85.7²
The value of h from the equation is equal to 106.0 miles.
Answer:
The probability is 0.9938
Step-by-step explanation:
In this question, we are asked to calculate the probability that the mean blood pressure readings of a group of people is less than a certain reading.
To calculate this, we use the z score.
Mathematically;
z = (mean - value)/(standard deviation/√N)
From the question, we can identify that the mean is 125, the value is 123 , the standard deviation is 9.6 and N ( total population is 144)
Let’s plug these values;
z = (125-123)/(9.6/√144) = 2.5
Now we proceed to calculate the probability with a s score less than 2.5 using statistical tables
P(z<2.5) = 0.9938
