The probability that a randomly chosen bolt has a width between 944 and 957 mm is 0.4796. The appropriate value for c is such that a randomly chosen bolt has a width less than c with a probability of 0.8508 is 962.4.
Probability is the branch of discrete mathematics. It is used for calculating how likely an event is to occur or happen.
As per the given question,
a.) Probability ( 944 < x < 957 ) = P[(944 - 952)/10 < (x-μ)/σ < (957 - 952)/10)]
= P ( -0.8 < z < 0.5 )
= P( z < 0.5 ) - P( z < -0.8 )
Probability ( 944 < x < 957 ) = 0.4796
b.) P( z < 1.04 ) = 0.8508
By the z-score formula,
⇒ c = z × σ + μ
= 1.04 × 10 + 952
c = 962.4
Therefore, The probability between 944 and 957 mm is 0.4796. The appropriate value for c with a probability of 0.8508 is 962.4.
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