Answer:
The Confidence Interval is (227.96 , 248.84)
Step-by-step explanation:
The sample size is given as n = 61
The average pressure is given as [tex]\mu[/tex] = 238.4 pounds
The standard deviation is given to be [tex]\sigma[/tex] = 35 pounds
The data collected for the radial tires is considered to be normally distributed.
Since the population is normally distributed the sample is also normally distributed, therefore [tex]\bar{x}[/tex] = [tex]\mu[/tex] =238.4 pounds
The confidence interval is given as C.I. = 98% = 0.98
Therefore the Significance Level, [tex]\alpha[/tex] = 1 - 0.98 = 0.02
Critical Z value is given as [tex]Z_{\frac{\alpha}{2}} = Z_{\frac{0.02}{2} } = Z_{0.01}[/tex] = [tex]\pm 2.33[/tex]
The Confidence Interval is given by the formula CI = [tex]\bar{x} \pm \{Z_{0.01}\frac{\sigma}{\sqrt{n} }\}[/tex]
Therefore C.I. = [tex]238.4 \pm \{ 2.33 \times \frac{35}{\sqrt{61} } \}[/tex]
= 238.4 ± 10.441
= 227.96 , 248.84
