Question

1. In an effort to determine how long phone customers are kept on hold, one airline took a random sample of 167 phone calls and determined the length of time in minutes each caller was kept on hold. The sample standard deviation was 3.8 minutes. How many more phone customers should be included in the sample to be 99% sure that the sample mean x of hold times is within 3o second of the population mean µ of hold times? 11 Normal Approximation to the Binomial Distribution.

please show all graphs and work

2. Quality control reports that 20% of ovens have faulty control panels. The owner of an apartment complex has just purchased 120 of these ovens. (a) Calculate the probability that less than 35 of them have a faulty control panels. (b) Calculate the probability that more than 25 of them have a faulty control panels

please show all graphs and work thank you

Answer 1

1) At 99% confidence interval the critical value is t^* = 2.606

30 sec = 0.5 min

Margin of error = 0.5

or, t^* * s/$\sqrt n$ = 0.5

or, 2.606 * 3.8/$\sqrt n$ = 0.5

or, n = (2.606 * 3.8/0.5)^2

or. n = 393

2) n = 120

    p = 0.2

$\mu$ = n * p = 120 * 0.2 = 24

$\sigma$ = sqrt(np(1 - p))

    = sqrt(120 * 0.2 * 0.8)

    = 4.382

a) P(X < 35)

= P(X < 34)

= P(X < 34.5)

= P((X - $\mu$)/$\sigma$< (34.5 - $\mu$)/$\sigma$)

= P(Z < (34.5 - 24)/4.382)

= P(Z < 2.4)

= 0.9918

b) P(X > 25)

= P(X > 26)

= P(X > 25.5)

= P((X - $\mu$)/$\sigma$> (25.5 - $\mu$)/$\sigma$)

= P(Z > (25.5 - 24)/4.382)

= P(Z > 0.34)

= 1 - P(Z < 0.34)

= 1 - 0.6331

= 0.3669