The weight of a medium-sized orange selected at random from a large bin of oranges at a local supermarket is a normally distributed random variable with mean μ = 12 ounces and standard deviation σ = 1.2 ounces. suppose we independently select two oranges at random from the bin. what is the probability that the difference in the weights of the two oranges exceeds 3 ounces?

0.0392

Step-by-step explanation:

The weight is normally distributed with :

Mean (\mu)= 12 ounces

Standard deviation (\sigma ) = 1.2 ounces

Let X_1 be the weight of first orange and X_2 be the weight of second orange.

Let X be the difference of the weight of two oranges (X_1-X_2)

X_1(12,1.2^{2}) and X_2(12,1.2^{2})

X(12-12,√1.2^{2}+1.2^{2}) = X(0,1.6971)

We need to calculate P(X>3) = 1-P(X≤3)

For calculating P(X≤3) in normal distribution, we use

Z =

 =  

 = 1.7677

P(Z≤ 1.7677) = 0.9608 (From normal distribution table)

P(X > 3) = 1-0.9608

            = 0.0392

the best buy, is the 4- kilogram bag of lollipops for $18.40.

step-by-step explanation:

i found my answer by dividing the cost of each bag by their respective weights.

14.88 divided by 2 = 7.44

17.29 divided by 3 = 5.77

18.4 divided by 4 = 4.6

24.4 divided by 5 = 4.88

by this, i found that the 4 kilo bag is the best buy.

the polynomial is a perfect square trinomial of the form a^2-2ab+b^2:

option a. true

step-by-step explanation:

9x^2-12x+4

comparing with the form a^2-2ab+b^2

1.) a^2=9x^2

solving for a: square root both sides of the equation:

sqrt(a^2)=sqrt(9x^2)

a=sqrt(9) sqrt(x^2)

a=3x

2.) b^2=4

solving for b: square root both sides of the equation:

sqrt(b^2)=sqrt(4)

b=2

to be a perfet square trinomial 2ab must be equal to 12x. let's check:

2ab = 2 (3x) (2)

2ab = 12x

correct