\"Durable press\" cotton fabrics are treated to improve their recovery from wrin

Question

"Durable press" cotton fabrics are treated to improve their recovery from wrinkles after washing. Unfortunately, the treatment also reduces the strength of the fabric. The breaking strength of untreated fabric is normally distributed with mean 51/2 pounds and standard deviation 2.7 pounds. The same type of fabric after treatment has normally distributed breaking strength with mean 26.1 pounds and standard deviation 1.9 pounds. A clothing manufacturer tests 5 specimens of each fabric. All 10 strength measurements are independent. (Round your answers to four decimal places.) (a) What is the probability that the mean breaking strength of the 5 untreated specimens exceeds 50 pounds? _______ b) What is the probability that the mean breaking strength of the 5 untreated specimens is at least 25 pounds greater than the mean strength of the 5 treated specimens? _________

Explanation / Answer

a)here for sample size n=5 ; std error for untreated specimens =std deviation/(n)1/2 =2.7/(5)1/2 =1.2075

therefore required probability =P(X>50)=P(Z>(50-51.2)/1.2075)=P(Z>-0.9938)=0.8398

b)

mean difference between untreated and treated specimens =51.2-26.1=25.1

std error of differnece =(2.72/5+1.92/5)1/2 =1.4765

therefore required probability =P(X>25)=P(Z>(25-25.1)/1.4765)=P(Z>-0.0677)=0.5270

please revert for any clarification required

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