The probability that the sample mean will be between 1195 and 1205 is 0.445
What is a probability distribution?
In mathematics, a probability distribution is a function that expresses the likelihood of many possible values for a variable. Graphs and probability tables are common ways of displaying probability distributions.
Given, mean = [tex]\mu[/tex] = 1200
standard deviation = [tex]\sigma[/tex] = 60
n = 50
[tex]\mu_{\bar x} = 1200\\\sigma_{\bar x} =\sigma / \sqrt(n) = 60/ \sqrt50=8.485[/tex]
[tex]P(1195 < \bar x < 1205 ) = P[(1195-1200) / 8.485 < (\bar x - \mu\bar x ) / \sigma\bar x < (1205-1200) / 8.485)][/tex]
= P(-0.59 < Z <0.59 )
= P(Z <0.59 ) - P(Z <-0.59 )
Using the z table, we get
=0.7224-0.2776
=0.4448 = 0.445 ( rounded to 3 decimal places)
Hence, the probability that the sample mean will be between 1195 and 1205 is 0.445
To learn more about a probability distribution
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