Write 7.264 51 correct to 3 decimal places
2 answers:
ANSWER
correct to 3 decimal places is
EXPLANATION
We start counting from the first number after the decimal point.
So starting from 2, we count 3 decimal places to the right and land on 4.
Next, we check to see if the number after 4, is greater or equal 5, then we round up, else we round down.
Since that number is 5, it is greater than or equal to 5.
Therefore we round up to obtain
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Answer:
P(35.3 < M < 35.4) = 0.0040.
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:
Find the probability that a single randomly selected value is between 35.3 and 35.4
This is the pvalue of Z when X = 35.4 subtracted by the pvalue of Z when X = 35.3. So
X = 35.4
By the Central Limit Theorem
has a pvalue of 0.9927
X = 35.3
has a pvalue of 0.9887
0.9927 - 0.9887 = 0.0040
So the answer is:
P(35.3 < M < 35.4) = 0.0040.