Answer:
Step-by-step explanation:
Hello!
X₁: Life span of a battery of Brand X
X₁~N(μ₁;σ₁²)
μ₁= 102hours
σ₁= 6.8hours
X₂: Life span of a battery of Brand Y
X₂~N(μ₂;σ²)
μ₂= 100hours
σ₂= 1.4hours
To complete the first two sentences, you have to use the empirical rule:
μ±δ= 68% of the distribution
μ±2δ= 95% of the distribution
μ±3δ= 99% of the distribution
1. About 68% of brand x’s batteries have a lifespan between <u>95.2 </u>and <u>108.8 hours</u>.
μ₁±σ₁= 102 ± 6.8= 95.2; 108.8
2. About 68% of brand y’s batteries have a lifespan between <u>98.6 </u>and <u>101.4 hours</u>.
μ₂±σ₂= 100 ± 1.4= 98.6; 101.4
3. The life span of brand <u> </u><u>Y </u>’s battery is more likely to be consistently close to the mean.
The standard deviations show you the dispersion of the distribution. A low standard deviation indicates that the values are close to the mean. A high standard deviation indicates that the values are further away the values are from the mean.
The standard deviation for the X batteries is σ₁= 6.8hours and the Y batteries are σ₂= 1.4hours since the standard deviation for the Y batteries is less than the standard deviation for the X batteries, you'd expect that the life span of the Y batteries will be closer to the mean than the life span of the X batteries.
I hope it helps!
