What Is the Probability of 50 Bombs Landing Within 10 Meters of the Target?

[gkraju]

Homework Statement

assume the dispersion of 3000 bombs launched from an aircraft showed a normally distributed miss distance profile with standard deviation of 10 meters. if 80 bobmbs are dropped on a target with no systematic errors at launch , what is probability that 50 bombs are within 10 meters of target.
Mean was not given but i think it should be assumed as zero

The Attempt at a Solution

mean = 0
std deviation = 10
x = 10
z1 = ( x - mean ) / std deviation

calculated p( z < z1) from normal distribution tables
then how to apply it for 50 bombs out of 80

 

[nilesh_pat]

?I think you are looking for the binomial probability. The probability that 50 out of 80 bombs will be within 10 meters of the target is given by: P = (80 choose 50) * 0.8413^50 * 0.1587^30 where 0.8413 is the probability that one bomb is within 10 meters of the target and 0.1587 is the probability that one bomb is not within 10 meters of the target.