Question

The meat department of a local supermarket packages ground beef using meat trays of two sizes: 1 designed to hold 1 lb of meet and other hold 3lbs.A random sample of 35 packages in small meat trays produced weight with an average of 1.01 lbs and standard deviation
of 0.18 lbs.

For a 99% confidence interval for average weights of all packages sold in small meat trays, what is the lower limit?

a.
1.088 lbs

b.
0.546 lbs

c.
0.932 lbs

d.
1.01 lbs

Answer 1

Answer:

c) 0.932

99% confidence interval for average weights of all packages sold in small meat trays.

(0.932 ,1.071)

Step-by-step explanation:

Explanation:-

Given random sample of 35 packages in small meat trays produced weight with an average of 1.01 lbs. and standard deviation  of 0.18 lbs.

size of the sample 'n' = 35

mean of the sample x⁻= 1.01lbs

standard deviation of the sample 'S' = 0.18lbs

The 99% confidence intervals are given by

$(x^{-} - t_{\alpha } \frac{S}{\sqrt{n} } , x^{-} +t_{\alpha } \frac{S}{\sqrt{n} } )$

The degrees of freedom γ=n-1 =35-1=34

tₐ =  2.0322

99% confidence interval for average weights of all packages sold in small meat trays

$(1.01 - 2.0322 \frac{0.18}{\sqrt{35} } , 1.01+2.0322 \frac{0.18}{\sqrt{35} } )$

( 1.01 - 0.06183 , 1.01+0.06183)

(0.932 ,1.071)

Final answer:-

99% confidence interval for average weights of all packages sold in small meat trays.

(0.932 ,1.071)