Answer:
0.97547
Step-by-step explanation:
Given That:
Mean (m) = 102
Standard deviation (σ) = 12
Sample size (n) = 63
Probability that sample mean would differ from Population mean by less than 3.4 watts
P(m - s < X < m + s)
P(102 - 3.4 < Z < 102 + 3.4)
Using the Z formula :
Zscore = (x - m) / (σ/√n)
x = 102 - 3.4 = 98.6 ; x = 102 + 3.4 = 105.4
Z = (98.6 - 102) / (12/√63) = −2.248888
P(Z < - 2.2488) = 0.012263 (Z probability calculator)
Z = (105.4 - 102) / (12/√63) = 2.2488886
P(Z < 2.2488) = 0.98774 (Z probability calculator)
0.98774 - 0.012263 = 0.97547
