Question

Use the given values of n= 93 and p= 0.24 to find the minimum value that is not significantly​ low, μ- 2σ ​, and the maximum value that is not significantly​ high, μ+2σ. Round your answer to the nearest hundredth as needed.

a. Minimum: 30.56; maximum: 14.08
b. Minimum: 14.08; maximum: 30.56
c. Minimum: 18.2; maximum: 26.44
d. Minimum:-11.61; maximum: 56.25

Answer 1

The answer is "Option a".

Explanation:

`n= 93 \\\\p= 0.24\\\\\mu=?\\\\ \sigma=?\\\\`

Using the binomial distribution:
`\mu = n* p = 93 * 0.24 = 22.32\\\\\sigma = √(n * p * (1-p))=√(93 * 0.24 * (1-0.24))=4.1186`

In this the maximum value which is significantly​ low,
`\mu-2\sigma`, and the minimum value which is significantly​ high,
`\mu+2\sigma`, that is equal to:

`\mu-2\sigma = 22.32 - 2(4.1186) = 14.0828 \approx 14.08\\\\\mu+2\sigma = 22.32 + 2(4.1186) = 30.5572 \approx 30.56`