The estimated mean lifetime of a bulb of 154.69
The table is given as:
Lifetime Frequency
25 < t ≤ 50 47
50 < t ≤ 100 86
100 < t ≤ 150 45
150 < t ≤ 200 36
200 < t ≤ 250 0
250 < t ≤ 300 37
300 < t ≤ 350 50
Calculate the midpoint using:
x = (Lower +Upper)/2
So, we have:
Lifetime Frequency
37.5 47
75 86
125 45
175 36
225 0
275 37
325 50
The mean value is calculated as:
[tex]\bar x = \frac{\sum fx}{\sum f}[/tex]
So, we have:
[tex]\bar x = \frac{37.5 * 47 + 75 * 86 + 125 * 45 + 175 * 36 + 225 * 0 + 275 * 37 + 325 * 50}{47 + 86 + 45 + 36 + 0 + 37 + 50}[/tex]
Evaluate
[tex]\bar x = \frac{46562.5}{301}[/tex]
Divide
[tex]\bar x = 154.69[/tex]
Hence, the estimated mean lifetime of a bulb of 154.69
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