DOING A QUIZ ASAP PLS
2 answers:
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Answer:
were u looking for some like this, its for the first question
Step-by-step explanation:
Z value is a numerical measurement that describe a value relationship to the mean of a group of values. The standard deviations is 1.25 above the mean is 14,500 hours.
<h3>Given information-</h3>The mean for the bulb is 12,000 hours.
The standard deviation for the bulb is 2000 hours.
Sample value is 14500.
To find out the how many standard deviation is 14500 mean away from the mean the z value of the mean should be calculated.
<h3>Z value</h3>Z value is a numerical measurement that describe a value relationship to the mean of a group of values. Z value is the ratio of the difference of the sample value and mean
to the standard deviation. Thus the z value for the given mean
is,
Thus the standard deviations is 1.25 above the mean is 14,500 hours.
Learn more about the z value here;
Answer:
a) 33% probability that a single student randomly chosen from all those taking the test scores 21 or higher.
b) 0.39% probability that the mean score for 76 students randomly selected from all who took the test nationally is 20.4 or higher
Step-by-step explanation:
To solve this question, we need 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 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.
Central limit theorem:
The Central Limit Theorem estabilishes that, for a random variable X, with mean and standard deviation
, the sample means with size n of at least 30 can be approximated to a normal distribution with mean
and standard deviation
In this problem, we have that:
a) What is the probability that a single student randomly chosen from all those taking the test scores 21 or higher?
This is 1 subtracted by the pvalue of Z when X = 21. So
has a pvalue of 0.67
1 - 0.67 = 0.33
33% probability that a single student randomly chosen from all those taking the test scores 21 or higher.
b) The average score of the 76 students at Northside High who took the test was x =20.4. What is the probability that the mean score for 76 students randomly selected from all who took the test nationally is 20.4 or higher?
Now we have
This probability is 1 subtracted by the pvalue of Z when X = 20.4. So
By the Central Limit Theorem
has a pvalue of 0.9961
1 - 0.9961 = 0.0039
0.39% probability that the mean score for 76 students randomly selected from all who took the test nationally is 20.4 or higher