Answer :
The probability that the sample mean will be between 295 to 305 is 0.99921
Since we are given that the mean is 300 and the standard deviation of 18 and we were given a total of 144 observations.A z-score gives you a thought of how distant from the mean a data point is. A z-score can be put on a normal distribution curve. Z In arrange to utilize a z-score, you wish to know the mean μ additionally the population standard deviation σ.
The formula we are referring to for calculating the Zscore is :
Zscore = (x - mean) ÷ σ/√n
At first, let x be = 295, so the
Zscore = (295 - 300) / (18/12) = - 3.33
The probability for zscore for z<-3.33 is,
=>P(Z< - 3.33) = 0.00039
Similarly for the second part x 305, Sp
The Zscore will be (305 - 300) / (18/12) = 3.33
so the probability of z<3.33
=>P(Z< 3.33) = 0.9996
so the probability of mean between the range 295 to 305
P(Z < 3.33) - P(Z < - 3.33)
=0.9996-0.00039
= 0.99921
To know more about zscore refer to the link https://brainly.com/question/25668280?referrer=searchResults.
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