a)
For a normal distribution, the Z score can be computed using the formula
The Z score is calculated as follows
Z = 0.61237
By looking at the Z score table for a value of 0.61237
The probability the proportion of successes in the sample will be less than 0.41 is 0.7291
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b)
At first we have to find the probability proportion of successes in the sample that will be less than 0.42
Z = 1.22
By looking at the Z score table for a value of 1.22
Probability the proportion of successes in the sample will be less than 0.42 equals 0.88877
Probability the proportion of successes in the sample will be greater than 0.42 = 1 - 0.88877
Probability the proportion of successes in the sample will be greater than 0.42 = 0.1112
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