question archive Using technology, use the normal approximation to find the indicated probability
Using technology, use the normal approximation to find the indicated probability
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Using technology, use the normal approximation to find the indicated probability. The sample size is n, the population proportion of successes is p, and X is the number of successes in the sample.
n = 104, p = 0.7: P(65 ≤ X ≤ 77)
Question 13 options:
A: 0.1573
B: 0.0379
C: 0.8049
D: 0.8427
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According to the question,
Given,
n = 104
p = 0.7
p = Probability of success
q = 1 - p = 0.3
μ = Mean
= np
= 104 * 0.7
= 72.8
σ2 = Variance
= npq
= 104 * 0.7 * 0.3
σ2 = 21.84
σ = 4.6733
To find P(65 ≤ X ≤ 77)
= P[65 - 72.8 / 4.6733 < X - 72.8 / 4.6733 < 77 - 72.8 / 4.6733]
= P[-7.8 / 4.6733 < Z < 4.2 / 4.6733]
= P[-1.6690 < Z < 0.8987]
= P[Z < 0.90] - P[-1.67]
= 0.8389 - 0.0367
= 0.8022
≈ 0.8049
