Mathematics, 15.04.2020 02:55, rairaibabycakez9578

Assuming you obtained a random sample of blood glucose levels from 32 individuals from a population and the mean of the population is 120 and the standard deviation of the sample is 15, calculate the probability that the mean blood glucose levels for the sample population will be above 127.

A. .9959
B. .5900
C. .4100
D. .0041

Answers: 1

Show answers

Answers

The option C) 0.0041 is correct∴ the probability that the mean blood glucose levels for the sample population will be above 127 is 0.0041.

Step-by-step explanation:

Given that Assuming you obtained a random sample of blood glucose levels from 32 individuals from a population and the mean of the population is 120 and the standard deviation of the sample is 15,

To calculate the probability that the mean blood glucose levels for the sample population will be above 127:

By using the Normal probability distribution and the Central limit theorem.

Normal probability distribution:

Problems of normally distributed samples are solved using the z-score formula.

In a given data set with mean $\mu$ and standard deviation $\sigma$ , the z-score of a measure X is given by:

$Z=\frac{x-\mu}{\sigma}$

Total probability=p+q=1

Subtracting 1 by the p value, we get the probability that the value of the measure is greater than X.

Central Limit Theorem :

The Central Limit Theorem states that, for a normally distributed random variable X, with mean $\mu$ and standard deviation $\sigma$ , the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean

For a skewed variable, the Central Limit Theorem for n is greater than 30.

Given that $\mu=120$ , $\sigma=15$ , n=32

$s=\frac{15}{\sqrt{32}}$

$s=\frac{15}{4(\sqrt{2})}$

s=2.65

Now we have to Calculate the probability that the mean blood glucose levels for the sample population will be above 127.

This is 1 subtracted by the p value of Z when X = 127.

$Z=\frac{x-\mu}{\sigma}$

By the Central Limit Theorem

$Z=\frac{x-\mu}{s}$

Substitute the values in the formula we get

$Z=\frac{127-120}{2.65}$

$=\frac{7}{2.65}$

Z=2.6415 has a p value of 0.9959

Now 1 subtracted by the p value of Z is 2.6415 when X = 127 is

1 - 0.9959 = 0.0041

∴ the probability that the mean blood glucose levels for the sample population will be above 127 is 0.0041.∴ option C) 0.0041 is correct.

answered: Guest

answer: answer: d) v= 1/6 bh

step-by-step explanation:

since according to the given question, a pyramid is placed inside a prism.

step-by-step explanation:

answered: Guest

step-by-step explanation:

Which of the following statements are true for the image of a triangles after a dilation that has a

Other questions on the subject: Mathematics

Mathematics, 21.06.2019 17:30, AzuraSchaufler

The graph below represents the number of dolphins in a dolphin sanctuary. select all the key features of this function.

Answers: 2

continue

Mathematics, 21.06.2019 18:00, tatibean26

The ratio of wooden bats to metal bats in the baseball coach’s bag is 2 to 1. if there are 20 wooden bats, how many metal bats are in the bag?

Answers: 1

continue

Mathematics, 21.06.2019 19:20, TrudnEli1217

Which number completes the system of linear inequalities represented by the graph? y> 2x – 2 and x + 4y 2 et 2 3 4

Answers: 3

continue

Mathematics, 21.06.2019 19:50, khenalilovespandas

Type the correct answer in each box. spell all words correctly. a sequence of transformations maps ∆abc onto ∆a″b″c″. the type of transformation that maps ∆abc onto ∆a′b′c′ is a . when ∆a′b′c′ is reflected across the line x = -2 to form ∆a″b″c″, vertex of ∆a″b″c″ will have the same coordinates as b′.

Answers: 1

continue

Do you know the correct answer?

Assuming you obtained a random sample of blood glucose levels from 32 individuals from a population...