Question

3 points) Fluorescent lighbulbs have lifetimes that are normally distributed with a mean of 6.6 years and a standard deviation of 1.3 years. The figure below shows the distribution of lifetimes of fluorescent lightbulbs. Calculate the shaded area under the curve. Express your answer in decimal form with at least two decimal place accuracy.

Answer 1

The shaded area under the curve is 0.597723.

We are to calculate the shaded area under the graph curve.

Information Given

Mean = 6.6

Standard deviation = 1.3

X ⇔ N (μ=6.6, σ=1.3)

= P [5.229 < X < 7.4]\

= P {{5.229-6.6} / 1.3} < Z < [{7.4-6.6}/1.3}]

= P {-0.857 <Z < 0.615}

=P[Z≤0.615} - P[Z≤-0.867}

We are using the normal probability table.

= 0.730723 - 0.133

= 0.597723

Therefore, the shaded area under the curve is 0.597723.

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