The famous physicist, Ernest Rutherford, was a pioneer in the study of radioactivity using electricity. In one experiment he observed the number of particles reaching a counter during time 1700 intervals of 7.5 seconds each. The number of intervals that had 0 - 4 particles reaching the counter is given in the table below. 
Let the random variable x = number of particles counted in a 7.5 second time period. 
Probability histogram 
b)Using the estimated probabilities in part (a), estimate the following:
i)P(x = 1), the probability that 1 particle was counted in 7.5 seconds.
ii)P(x < 3), the probability that fewer than 3 particles were counted.
iii)P(x ≥ 3), the probability that at least 3 particles were counted.
Definitions:
Elements of Caring Leadership
Traits or behaviors exhibited by leaders that demonstrate concern and empathy for subordinates.
Uncompensated Work Time
Time spent working for which an individual does not receive payment or formal recognition.
Headaches
A common physical ailment characterized by pain in the head or face, often associated with tension, stress, or medical conditions.
Loneliness
A state of detachment, separation, and isolation; a feeling of being friendless and forlorn.
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