Question

a. Electrical resistors having a mean resistance of 30 ohms and a standard deviation of 3 ohms, what is the probability that a random sample of 29 resistors will have a combined resistance of more than 900 ohms?

b. A tire manufacturer determines at what temperature the tires will tend to bubble. In a sample of 75 tires, the mean temperature was 120 degrees F. The manufacturer assumes that the standard deviation of this temperature from all tires is 12 degrees. Construct the 98% confidence interval for the population mean.

Answer 1

a) Electrical resistors having a mean resistance of 30 ohms and a standard deviation of 3 ohms.

the probability that a random sample of 29 resistors will have a combined resistance of more than 900 ohms is,

  

$=P(\frac{X-30}{3} > \frac{900-30}{3})$

  

= P(Z > 290)

  $=1-P(Z \leq 290)$ = 1-1 = 0 (ans)

b)  In a sample of 75 tires, the mean temperature was 120 degrees F. The manufacturer assumes that the standard deviation of this temperature from all tires is 12 degrees.

98% Confidence Interval is given by,

  $\bar{x}\pm z^{*} \frac{s}{\sqrt{n}}$

$=(120\pm 2.33 \frac{12}{\sqrt{75}})$

= ( 116.77 , 123.23 )

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