Question

The scores on Quiz 2 follows the normal distribution with a mean of 8 and a standard deviation of 0.5.What is the probability that a randomly selected student has a score below 5?

You have an answer but with the z table score approach and the teach is saying that it should be equal to 0.000000000987

Answer 1

Solution :

Given that,

mean = = 8

standard deviation = =0.5   

P(X<5 ) = P[(X- ) / < (5 -8) /0.5 ]

= P(z <-6 )

Using z table

probability = 0.0 approximately 0

Answer 2

To find the probability that a randomly selected student has a score below 5 in a normal distribution with a mean (μ) of 8 and a standard deviation (σ) of 0.5, we can use the z-score approach.

The z-score formula is given by: z = (X - μ) / σ

where: X is the value we want to find the probability for (in this case, X = 5), μ is the mean of the distribution (μ = 8), σ is the standard deviation of the distribution (σ = 0.5), and z is the z-score.

Now, let's calculate the z-score for X = 5: z = (5 - 8) / 0.5 z = -6

Next, we need to find the probability of having a z-score of -6. For this, we can refer to a z-table or use statistical software.

From the z-table, the probability of having a z-score less than -6 is essentially 0 (usually given as 0.000000 or something similar in scientific notation).

Therefore, the probability that a randomly selected student has a score below 5 is very close to 0, or approximately 0.00000000098, as your teacher mentioned. It's an extremely low probability due to the significant difference between the mean and the value