The mean no. of defective apples in tray is 7.8 and the variance is 2.73. find the probability that there are exactly 4 defective apples in the tray. state the assumptions
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Given:
Mean number of defective apples in tray is 7.8
Variance is 2.7
To find:
The probability that there are exactly 4 defective apples in the tray
Answer:
- Given that, variance is 2.7
- Standard deviation (SD) = √variance = √2.7 = 1.64
- Let us assume that the distribution is normal.
- z = (x - mean)/ SD
- Here x is the number of defective apples in the tray = 4
- z = (4 - 7.8)/1.64 = -2.317
- P (0<z<-2.317) = 0.4898
- P (z=-2.317) = 0
- P (x=4) = 0
Thus, the probability that there are exactly 4 defective apples in the tray is 0.
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