Answer:
Range = 29
Variance= (X₁- U) ² / N= 973/10 = 97.3
Standard Deviation= √variance= √97.3= 9.864
Step-by-step explanation:
Range = Difference between the highest and lowest value = 97-68= 29
Variance
X₁ X₁-U (X₁- U) ²
80 0 zero
68 -12 144
71 -9 81
72 -8 64
95 15 225
89 9 81
97 17 289
72 -8 64
75 -5 25
81 1 1
∑ 800 ZERO 973
u= ∑X₁ /10=800/10=80
Variance= (X₁- U) ² / N= 973/10 = 97.3
Standard Deviation= √variance= √97.3= 9.864
(b) The important feature of the data is not revealed through the different measures of variation is that the variability of two or more than two sets of data cannot be compared unless a relative measure of dispersion is used .
P(<em>X</em> ≤ 65) = P((<em>X</em> - 79)/7 ≤ (65 - 79)/7) = P(<em>Z</em> ≤ -2)
where <em>Z</em> follows the standard normal distribution with mean 0 and standard deviation 1.
Recall that for any normal distribution with mean <em>µ</em> and s.d. <em>σ</em>, we have
P(|<em>X</em> - <em>µ</em>| ≤ 2<em>σ</em>) ≈ 0.95
which in the case of <em>Z</em> translates to
P(-2 ≤ <em>Z</em> ≤ 2) ≈ 0.95
Now,
P(-2 ≤ <em>Z</em>) + P(-2 ≤ <em>Z</em> ≤ 2) + P(<em>Z</em> ≥ 2) = 1
==> P(-2 ≤ <em>Z</em>) + P(<em>Z</em> ≥ 2) ≈ 0.05
Any normal distribution is symmetric about its mean, so P(-2 ≤ <em>Z</em>) = P(<em>Z</em> ≥ 2), and this gives us
==> 2 P(-2 ≤ <em>Z</em>) ≈ 0.05
==> P(-2 ≤ <em>Z</em>) ≈ 0.025
Answer:
how is this a math question lol