Question

The Ball Corporation's beverage can manufacturing plant in Fort Atkinson, Wisconsin, uses a metal supplier that provides metal with a known thickness standard deviation σ = 0.000786 mm. Assume a random sample of 55 sheets of metal resulted in an x¯ = 0.3307 mm. Calculate the 98 percent confidence interval for the true mean metal thickness. (Round your answers to 4 decimal places.) The 98% confidence interval is from to

Answer 1

Solution :

Given ,

= 0.3307

= 0.000786

n = 55

At 98% confidence level the z is ,

  = 1 - 98% = 1 - 0.98 = 0.02

/ 2 = 0.02 / 2 = 0.01

Z_/2 = Z_0.01 = 2.326

Margin of error = E = Z_/2* ( /n)

= 2.326 * (0.000786 / 55)

= 0.000247

At 98% confidence interval estimate of the mean is,

- E < < + E

0.3307 - 0.000247 < < 0.3307 + 0.000247

0.3305 < < 0.3309

(0.3305, 0.3309)

The 98% confidence interval is from 0.3305 to 0.3309