Which of the following numbers could not

possibly be probabilities?
justify your answer

a)0.124
b)1
c)-0.1142
d)0
e)2/7
f)6/5
g)2.8

Assume that the mean score on a certain aptitude test across the nation is 100, and that the standard deviation is 20 points. Find the probability that the mean aptitude test score for a randomly selected group of 150 8th graders is between 99 and 101

What on earth could a negative probability mean ?

How can you have two probabilities more than 100%

To determine which of the following numbers could not possibly be probabilities, let's first establish what a probability is. In probability theory, a probability represents the likelihood of an event occurring. Probabilities are always non-negative numbers between 0 and 1, inclusive.

Now, let's go through each option and analyze whether it meets the conditions for being a probability:

a) 0.124: Since this number is between 0 and 1, it could be a valid probability.

b) 1: This number represents certainty, which means the event is guaranteed to occur. Therefore, it is a valid probability.

c) -0.1142: Probabilities cannot be negative, so this number could not be a probability.

d) 0: This number represents impossibility, meaning the event will not occur. Therefore, it is a valid probability.

e) 2/7: This fraction represents the ratio of successful outcomes to the total number of possible outcomes. As long as both the numerator and denominator are non-negative numbers, this fraction could be a valid probability.

f) 6/5: Since the numerator is greater than the denominator, this fraction is larger than 1. Since probabilities must be between 0 and 1, it could not be a valid probability.

g) 2.8: Similar to option f, this number is greater than 1 and therefore could not be a valid probability.

In summary, the numbers that could not possibly be probabilities are c) -0.1142, f) 6/5, and g) 2.8.