This table shows numbers of sweets in some tubes, but a coffee stain has deleted one of the figures.
1 answer:
To get the answer, you need to think of it like a see-saw.
Both sides must equal the same relative to 33.5. For example, 32 is 1.5 away from 33.5 so you could say you have 1.5*4 (because theres 4 tubes with 32 sweets). If you were to do this for the whole table, it would look something like this:
This simplifies to:
This method can sometimes be inefficient depending on how many values but is probably the simplest way to solve this problem.
hope this helps :)
(sorry the other way is kinda hard to explain possibly ask your teacher tomorrow)
Both sides must equal the same relative to 33.5. For example, 32 is 1.5 away from 33.5 so you could say you have 1.5*4 (because theres 4 tubes with 32 sweets). If you were to do this for the whole table, it would look something like this:
This simplifies to:
This method can sometimes be inefficient depending on how many values but is probably the simplest way to solve this problem.
hope this helps :)
(sorry the other way is kinda hard to explain possibly ask your teacher tomorrow)
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Answer:
0.0721 = 7.21% probability that the mean height for the sample is greater than 65 inches.
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 normal distributions can be solved using the z-score formula.
In a set with mean and standard deviation
, the z-score 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 p-value, we get the probability that the value of the measure is greater than X.
Central Limit Theorem
The Central Limit Theorem establishes that, for a normally distributed random variable X, with mean and standard deviation
, the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean
and standard deviation
.
For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.
Mean of 64.4 inches, standard deviation of 2.91
This means that
Sample of 50 women
This means that
What is the probability that the mean height for the sample is greater than 65 inches?
This is 1 subtracted by the p-value of Z when X = 65. So
By the Central Limit Theorem
has a p-value of 0.9279
1 - 0.9279 = 0.0721
0.0721 = 7.21% probability that the mean height for the sample is greater than 65 inches.