Denzel makes 10 of his first 50 shots in basketball free throw contest his success rate stays about the same for his next 100 free throws

P(z<-2.33 or z>2.66) = 0.0138

Step-by-step explanation:

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.

P(z<-2.33 or z>2.66)

P(z < -2.33)

Z = -2.33 has a pvalue of 0.0099. So

P(z < -2.33) = 0.0099.

P(z > 2.66)

1 subtracted by the pvalue of Z when X = 2.66.

Z = 2.66 has a value of 0.9961

P(z > 2.66) = 1 - 0.9961 = 0.0039

P(z<-2.33 or z>2.66) = P(z < -2.33) + P(z > 2.66) = 0.0099 + 0.0039 = 0.0138

P(z<-2.33 or z>2.66) = 0.0138