The number of candies in bags of the same size is normally distributed with a mean of 145 candies and a standard deviation of 3 candies.

there are 160 bags of candies on a shelf.

about how many bags of candies are expected to have between 142 candies and 148 candies?

a) 109
b) 119
c) 128
d) 133

The correct answer is A. 109

Step-by-step explanation:

1. Let's review all the information given to answer the question correctly:

Mean of candies in bags = 145

Standard deviation = 3

Number of bags of candies on a shelf = 160

2. About how many bags of candies are expected to have between 142 candies and 148 candies?

Let's recall that in a normal distribution, the 68.2% of the sample or the population is between minus one and plus one time the standard deviation.

For our case, the 68.2% of the bags of candies are expected to have between minus one time the standard deviation (145 - 3) and plus one time the standard deviation (145 + 3).

It means that 109 bags (0.682 * 160)  are expected to have between 142 and 148 candies. The correct answer is A. 109.

answer: a video game has three difficulty levels: easy, medium, and expert. the game's scoring works in such a way that a player has to score a fixed number of points to advance to the next level, and then the scoring starts over. the total score needed to clear all three difficulty levels is 7,500. two times the number of points needed to clear the easy level is 500 more than the number of points needed to clear the medium level. twice the number of points needed to clear the medium difficulty level is 1,500 more than the number of points needed to clear the expert level. if x, y, and z represent the easy, medium, and expert levels, respectively, and a is the coefficient matrix of the system of equations modeling this situation, identify the inverse matrix, a-1, and the solution matrix, x, of the system of equations.

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