Porphyrin is a pigment in blood protoplasm and other body fluids that is significant in body energy and storage. Let x be a random variable that represents the number of milligrams of porphyrin per deciliter of blood. In healthy circles, x is approximately normally distributed with mean µ = 43 and standard deviation σ = 15. Find the following probabilities. (Round your answers to four decimal places.) a. x is less than 60
b. x is greater than 16
c. x is between 16 and 60
d. x is more than 60

a) 0.8708 = 87.08% probability that x is less than 60

b) 0.9641 = 96.41% probability that x is greater than 16.

c) 0.8349 = 83.49% probability that x is between 16 and 60

d) 0.1292 = 12.92% probability that x is more than 60.

Step-by-step explanation:

When the distribution is normal, we use the z-score formula.

In a set with mean and standard deviation , the zscore of a measure X is given by:

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.

In this question, we have that:

a. x is less than 60

This is the pvalue of Z when X = 60. So

has a pvalue of 0.8708

0.8708 = 87.08% probability that x is less than 60

b. x is greater than 16

This is 1 subtracted by the pvalue of Z when X = 16. So

has a pvalue of 0.0359

1 - 0.0359 = 0.9641

0.9641 = 96.41% probability that x is greater than 16.

c. x is between 16 and 60

This is the pvalue of Z when X = 60 subtracted by the pvalue of Z when X = 16. We found those in a and b, si:

0.8708 - 0.0359 = 0.8349

0.8349 = 83.49% probability that x is between 16 and 60

d. x is more than 60

This is 1 subtracted by the pvalue of Z when X = 60.

So

1 - 0.8708 = 0.1292

0.1292 = 12.92% probability that x is more than 60.

4

step-by-step explanation:

a, b, c, d are correct.

step-by-step explanation:

we have g(x) = 3 and are required to find which option is a translation of g(x).

now, 'translation' is a transformation which means to shift the function in any direction and the general form of translation is g(x) + k, where k is any real number.

so, according to the options we see that all are correct as they satisfy the general form of translation.

also, it can be seen from the graph below that the function g(x) = 3 is shifted from its position in all the four options.