Respuesta :
The probability that the sample mean height will be less than 69 inches is 0.966 or 96.6%.
What is normal distribution?
The normal distribution, like any other probability distribution, defines how well the values of a statistic are distributed. Because it accurately captures the range of values for many natural occurrences, it is the most significant probability distribution in statistics.
The formula for normal distribution is;
[tex]Z=\frac{\bar{X}-\mu}{\left(\frac{\sigma}{\sqrt{n}}\right)}[/tex]
Where, X is the sample average( = 69).
μ is the mean (= 70).
σ is the standard distribution ( = 4)
n is the sample size (= 54).
Substituting above values in the formula;
[tex]z=\frac{69-70}{\left(\frac{4}{\sqrt{54}}\right)}[/tex]
z = -1.83
So the likelihood that it sample mean is less than 69 would be the probability of Z will be greater than -1.83 This is determined using the Z-table:
P( < 69) = P(Z < -1.83) = 0.966
Therefore, the probability for getting the sample mean height will be less than 69 inches is 0.966 or 96%.
To know more about the normal distribution, here
https://brainly.com/question/6476990
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