In this situation,
n=50, p=1/20, q=(1-p)=19/20, and npq=19/8=2.4
We would like np and npq to be a large number, at least greater than 10.
The normal approximation can always be applied, but the result will be very approximate, depending on the values of np and npq.
Situations are favourable for the normal approximation when p is around 0.5, say between 0.3 and 0.7, and n>30.
"Normal approximation" is using normal probability distribution to approximate the binomial distribution, when n is large (greater than 70) or exceeds the capacity of most hand-held calculators. The binomial distribution can be used if the following conditions are met:
1. Bernoulli trials, i.e. exactly two possible outcomes.2. Number of trials is known before and constant throughout the experiment, i.e. independent of outcomes.3. All trials are independent of each other.4. Probability of success is known, and remain constant throughout trials.
If all criteria are satisfied, we can model with binomial distribution, where the probability of x successes out of N trials each with probability of success p is given byP(x)=C(N,x)(p^x)(1-p)^(N-x)and,C(N,x) is number of combinations of selecting x objects out of N.
The mean is np, and variance is npq.
For the given situation, np=2.5, npq=2.375, so standard deviation=sqrt(2.375)=1.54.
Answer:
10 units
Step-by-step explanation:
Represent the length of the shortest side of the triangle by x. Then the sum of the lengths of the other two sides is 2(x + 1), and the perimeter of the triangle is thus x + 2(x + 1), or 3x + 2.
Represent the side length of the square by x - 2. Then the perimeter of the square is 2(x - 2) + 2(x - 2) = 4(x - 2) = 4x - 8, and this perimeter matches that of the triangle:
4x - 8 = 3x + 2, or
x = 10
The length of the shortest side of the triangle is 10 units.
Answer:
Step-by-step explanation:
Given data
Charge per movie= $2.95
monthly fee= $39.95
let the number of movies be x
Hence the expression for the total is given as
Answer:
The minimum amount of rubber needed is 1,134 square inches
Step-by-step explanation:
we know that
The surface area of a sphere (basketball ) is given by the formula
we have
----> the radius is half the diameter
substitute
Multiply by 4 (because are four basketballs)
therefore
The minimum amount of rubber needed is 1,134 square inches
