Answer:
0.9168
Step-by-step explanation:
From the data given:
Mean = 110
standard deviation = 5
Let consider a random sample n =49 which have a mean between 109 and 112.
The test statistics can be computed as:
[tex]Z_1 = \dfrac{x- \bar x}{\dfrac{\sigma}{\sqrt{n}}}[/tex]
[tex]Z_1 = \dfrac{109- 110}{\dfrac{5}{\sqrt{49}}}[/tex]
[tex]Z_1= \dfrac{-1}{\dfrac{5}{7}}[/tex]
[tex]Z_1[/tex] = -1.4
[tex]Z_2= \dfrac{x- \bar x}{\dfrac{\sigma}{\sqrt{n}}}[/tex]
[tex]Z_2 = \dfrac{112- 110}{\dfrac{5}{\sqrt{49}}}[/tex]
[tex]Z_2 = \dfrac{2}{\dfrac{5}{7}}[/tex]
[tex]Z_2 =2.8[/tex]
Thus; P(109 < [tex]\overline x[/tex] < 112) = P( - 1.4 < Z < 2.8)
= P(Z < 2.8) - P( Z < -1.4)
= 0.9974 - 0.0806
= 0.9168
