Question

You have a mean of 51.4 and a standard deviation of 5.6 . Find the z score for a value of 58.4 . Then use the standard normal distribution to find the probability of getting a value larger than that given, i.e. find P(X>58.4). You can use R to find standard normal probabilities. The function in R is pnorm (z). For example, you find a z value of -1 and you want to find the probability of a z value being greater than -1 so you type 1 -pnorm (−1) into R and it returns the result 0.8413447 . Enter the probability, P(X>58.4)=P(Z> the z value you found ). *Note: Canvas is set to calculate an approximation to the correct value with an allowance for error that will ensure you get this correct if you have the actual correct value.

Answer 1

To find the z-score for a value of 58.4, we can use the formula:

z = (x - μ) / σ

where:

- z is the z-score

- x is the value we want to find the z-score for (58.4 in this case)

- μ is the mean (51.4 in this case)

- σ is the standard deviation (5.6 in this case)

Substituting the given values into the formula:

z = (58.4 - 51.4) / 5.6

z = 1.25

Next, we want to find the probability of getting a value larger than 58.4, which is equivalent to finding P(X > 58.4). Since the distribution is standard normal, we can use the standard normal distribution table or a statistical software like R.

Using R, we can find this probability by subtracting the cumulative probability from 1. The cumulative probability is given by the function pnorm(z). So, we can calculate P(X > 58.4) as follows:

P(X > 58.4) = 1 - pnorm(1.25)

Substituting the value into R or any statistical software, we can obtain the result.

Please note that due to the limitations of the platform, I am unable to directly use R to provide you with the exact probability. However, you can enter the value 1.25 into R using the pnorm function as explained above to obtain the probability.

I hope this explanation helps! Let me know if you have any further questions or need additional assistance.