14. if s and t are normal linear operators satisfying st*-ts and ts*=s*t, show that their sum s+t and product st are normal. 15. show that a bounded linear operator t: hh on a complex hilbert space h is normal if and only if llt*xll-itxll for all xe h. using this, show that for a normal linear operator,

22

step-by-step explanation:

x=6 and x=3

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d. 24+-0.114

step-by-step explanation:

the question requires us to calculate the approximate 95% confidence interval for the mean number of ounces of ketchup per bottle in the sample given the following statistics;

sample mean = 24

standard deviation, σ = 0.4

sample size , n = 49

the confidence interval for a population mean is calculated using the formula;

sample mean ± z-score*(σ/sqrt(n))

the z-score associated with a 95% confidence interval, from the standard normal tables, is;

1.96

substituting these values into the formula;

24 ± 1.96*(0.4/7)

= 24 ± 0.112

from the alternatives given, choice d is closest to the above expression;