Rosa’s work finding the median of a set of test scores is shown below.

The mean points obtained in an aptitude examination is 159 points with a standard deviation of 13 points. What is the probabilit

Korolek [52]

Answer:

0.4514 = 45.14% probability that the mean of the sample would differ from the population mean by less than 1 point if 60 exams are sampled

Step-by-step explanation:

To solve this question, we have to understand 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 set with mean $\mu$ and standard deviation $\sigma$ , the zscore of a measure X is given by:

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

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.

Central limit theorem:

The Central Limit Theorem estabilishes that, for a random variable X, with mean $\mu$ and standard deviation $\sigma$ , a large sample size can be approximated to a normal distribution with mean $\mu$ and standard deviation $s = \frac{\sigma}{\sqrt{n}}$

In this problem, we have that:

$\mu = 159, \sigma = 13, n = 60, s = \frac{13}{\sqrt{60}} = 1.68$

What is the probability that the mean of the sample would differ from the population mean by less than 1 point if 60 exams are sampled?

This is the pvalue of Z when X = 159+1 = 160 subtracted by the pvalue of Z when X = 159-1 = 158. So

X = 160

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

By the Central Limit Theorem

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

$Z = \frac{160 - 159}{1.68}$

$Z = 0.6$

$Z = 0.6$ has a pvalue of 0.7257

X = 150

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

$Z = \frac{158 - 159}{1.68}$

$Z = -0.6$

$Z = -0.6$ has a pvalue of 0.2743

0.7257 - 0.2743 = 0.4514

0.4514 = 45.14% probability that the mean of the sample would differ from the population mean by less than 1 point if 60 exams are sampled

7 0

3 years ago

3(x-7)+8=-20 can someone explain how to do this step by step

Mrrafil [7]

3(x-7)+8=-20

Multiply the bracket by 3

(3)(x)(3(-7)+8= -20

3x-21+8= -20

3x-13= -20

Move -13 to the other side. Sign changes from -13 to +13.

3x-13+13= -20+13

3x= -7

Divide by 3

3x/3= -7/3

x= -7/3 or in mixed number : -2 1/3

Answer : x= -7/3 or in mixed number : -2 1/3

3 0

3 years ago

Read 2 more answers

Captain Ben has a ship, the H.M.S Crimson Lynx. The ship is five furlongs from the dread pirate Luis and his merciless band of t

grigory [225]

Answer:

We can see that this is dependent probability. We can find dependent probability of happening event A then event B by multiplying probability of event A by probability of event B given that event A already happened.

Step-by-step explanation:

In our case event A is pirate hitting captain's ship and event B is captain missing pirate's ship. We have been given that pirate shoots first so pirate's ship can't be hit before pirate shoots his cannons. So probability of hitting captain's ship is 1/3. We have been given that if Captain Ben's ship is already hit then Captain Ben will always miss. So the probability of Captain missing the dread pirate's ship given the pirate Luis hitting the Captain ship is 1. Now to find probability that pirate hits Captain, but Captain misses we will multiply our both probabilities.

8 0

3 years ago

In the 2014 - 2015 school year, the mean score on the critical reading of the SAT was 490 with a standard deviation of 102 for j

bonufazy [111]

Answer:

The Ranking Percentile is (B) 97.5%

Explanation :

To find the percentile rank we need to find the z- score. After finding the z-score match this value with the corresponding value in z-score table.

Formula to find the z-score

Z-score= $\frac{\text { scored obtained - mean }(\mu)}{\text { standard deviation }(\sigma)}$