P(<em>X</em> ≤ 65) = P((<em>X</em> - 79)/7 ≤ (65 - 79)/7) = P(<em>Z</em> ≤ -2)
where <em>Z</em> follows the standard normal distribution with mean 0 and standard deviation 1.
Recall that for any normal distribution with mean <em>µ</em> and s.d. <em>σ</em>, we have
P(|<em>X</em> - <em>µ</em>| ≤ 2<em>σ</em>) ≈ 0.95
which in the case of <em>Z</em> translates to
P(-2 ≤ <em>Z</em> ≤ 2) ≈ 0.95
Now,
P(-2 ≤ <em>Z</em>) + P(-2 ≤ <em>Z</em> ≤ 2) + P(<em>Z</em> ≥ 2) = 1
==> P(-2 ≤ <em>Z</em>) + P(<em>Z</em> ≥ 2) ≈ 0.05
Any normal distribution is symmetric about its mean, so P(-2 ≤ <em>Z</em>) = P(<em>Z</em> ≥ 2), and this gives us
==> 2 P(-2 ≤ <em>Z</em>) ≈ 0.05
==> P(-2 ≤ <em>Z</em>) ≈ 0.025
Answer:
y=2/3
Step-by-step explanation:
Find two points on the line and find the slope.
1,-3 -1,1
y1-y2/x1-x2
-3-1/1--1
-3/2
Then find the reciprocal of this slope by flipping the numerator and the denominator, changing the sign from positive to negative and visa versa.
Step-by-step explanation:
linear equation formula
y = mx +b
where
b = y-intercept
m = slope
so 15 should be y=
16 should be
17 should be
18 should be
Answer:
the height of the mountain is 7.35 m
Step-by-step explanation:
Given;
final velocity of the man, v = 12 m/s
initial velocity of the man, u = 0
The height of the mountain is calculated as;
v² = u² + 2gh
v² = 0 + 2gh
v² = 2gh
h = v²/2g
h = (12)² / (2 x 9.8)
h = 7.35 m
Therefore, the height of the mountain is 7.35 m
Answer:
The probability of getting 4 or more days when the surf is at least 6 feet is 0.544
Step-by-step explanation:
We can modelate this exercise as a binomial random variable.
The probability function of a binomial random variable is :
Where is the probability of the variable X to assume the value r
nCr is the combinatorial number define as
n is the number of binomial experiments that we make. In our exercise, n is the number of random days we pick of January.
And finally p is the success probability.
In our exercise, we define X : ''The number of days when the surf is at least 6 feet''.
And we are looking for P(X≥4).
P(X≥4) = P(X = 4) + P(X = 5) + P(X = 6)
Finally
P(X≥4)=
P(X≥4) = 0.544