Question

1. delivery charges the average delivery charge for a refrigerator is $32. the standard deviation is $4. find the minimum percentage of data values that will fall in the range of $20 to $44. use chebyshevs theorem.

Explanation:

Step1: Calculate the value of \( k \)

Chebyshev's theorem formula is \( P(X:\mu - k\sigma<X<\mu + k\sigma)\geq1-\frac{1}{k^{2}} \).
First, find \( k \). Given \( \mu = 32 \), \( \sigma=4 \).
For the lower - bound: \( 32 - k\times4=20 \), so \( 4k = 32 - 20=12 \), then \( k = 3 \).
For the upper - bound: \( 32 + k\times4=44 \), so \( 4k=44 - 32 = 12 \), then \( k = 3 \).

Step2: Apply Chebyshev's theorem

Substitute \( k = 3 \) into the formula \( P(X:\mu - k\sigma<X<\mu + k\sigma)\geq1-\frac{1}{k^{2}} \).
We get \( P(X:20<X<44)\geq1-\frac{1}{3^{2}}=1-\frac{1}{9}=\frac{8}{9}\approx0.8889 = 88.89\% \).

Answer:

The minimum percentage of data values that will fall in the range of \( \$20 \) to \( \$44 \) is \( 88.89\% \).