85 EN PHYSIQUE Fonctionnement de l'ail

In Illinois, 10 % of all drivers arrested for DUI (Driving Under the Influence) are repeat offenders; that is, they have been ar

docker41 [41]

Answer:

a) P(X=5) = 0.065

b) P(X≥1) = 0.928

c) The mean number of repeat offenders is 3.

d) The standard deviation of the number of repeat offenders is 2.

Step-by-step explanation:

n = 25

p = 10% = 0.10

q = 1-p

= 1-0.1

q=0.9

a) Find P(X =5)

Using the binomial distribution formula:

P(X = x) = ⁿCˣ pˣ qⁿ⁻ˣ

where p = probability of success

q = probability of failure

n = total number of trials

x = no. of successful trials

P(X=5) = ²⁵C₅ (0.1)⁵ (0.9)²⁵⁻⁵

= 0.0645 ≅ 0.065

P(X=5) = 0.065

b) We need to find the probability that at least one person is a repeat offender which means at most there can be 25 repeat offenders hence, we need to compute the probability for all values ranging from 1 to 25. The easy way to solve this problem is to find out the probability of less than one repeat offender and then subtract the value from the total probability (i.e. 1).

P(X≥1) = 1 - P(X<1)

= 1 - P(X =0)

= 1 - ²⁵C₀ (0.1)⁰ (0.9)²⁵⁻⁰

= 1 - 0.072

P(X≥1) = 0.928

c) The mean of the binomial distribution is:

μ = np

So, the mean number of repeat offenders can be computed as:

μ = (25)(0.10)

μ = 2.5 ≅ 3

The mean number of repeat offenders is 3.

d) The standard deviation of the binomial distribution is:

σ = √npq

So, the standard deviation of the number of repeat offenders can be computed as:

σ = √(25)(0.1)(0.9)

= √2.25

σ = 1.5 ≅ 2

The standard deviation of the number of repeat offenders is 2.

7 0

2 years ago

Find the area of the parallelogram by finding the height of the 45 45 90 triangle

slavikrds [6]

Answer:

45 in²

Step-by-step explanation:

Since it's a 45-45-90 triangle, the legs are equal length. The legs are the sides that are not the hypotenuse. The hypotenuse is the side opposite the 90° angle. Here, the legs are both 6. This is also the height of the parallelogram.

The formula for area of a parallelogram is

A = LH where L is the side length, and H is the height

So the area is

A = 7.5(6) = 45 in²

6 0

3 years ago

A student has a 2% salt water solution and a 7% salt water solution. To best imitate salt water at a local beach, he needs 1 lit

FromTheMoon [43]

Let

x-------> the amount of $2\%$ solution