Question 1206571
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𝜇 = greek letter mu = mean = 1.48
𝜎 = greek letter sigma = standard deviation = 1.42


𝜇 ± 2𝜎 breaks down into 𝜇 - 2𝜎 and 𝜇 + 2𝜎


This will mean 𝜇 - 2𝜎 < x < 𝜇 + 2𝜎


𝜇 - 2𝜎 = 1.48 - 2*1.42 = -1.36
𝜇 + 2𝜎 = 1.48 + 2*1.42 = 4.32


We're focused on the interval -1.36 < x < 4.32


If x is an integer then we focus on the sub-interval {{{-1 <= x <= 4}}}
Furthermore, the smallest x can be in this case is x = 0, so we're really only going to focus on {{{0 <= x <= 4}}}


Add up the probability values associated with x = 0 through x = 4.
P(0)+P(1)+P(2)+P(4) = 0.35+0.2+0.19+0.17+0.06 = <font color=red>0.97</font> which is the final answer


Or as an alternate route
P(5) = 0.03
P(value between 0 and 4) = 1 - P(5) = 1 - 0.03 = <font color=red>0.97</font>


There's a 97% chance of picking an x value between 0 and 4 inclusive of both endpoints. 
This is equivalent to saying there's a 97% chance of picking an x value such that -1.36 < x < 4.32; where each endpoint is two standard deviations away from the mean.



Answer: <font color=red>0.97</font>
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