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(b) We require the probability that the number of heads will lie between 220 and 280 or, considering the data as continuous, between 219.5 and 280.5. 219.5 in standard units Required probability 219.5 250 11.18 2(0.4968) 0.9936 2.73 280.5 in standard units 0 and z 2.73 2.73)

Some two-port circuits or electronic devices are best characterized by the following terminal equations: V1 h11 I1 h12 V2 I2 h21 I1 h22 V2 where the hij coe cients are called the hybrid parameters, or h-parameters.

It follows that we can be very confident that the number of heads will not differ from that expected (250) by more than 30. Therefore, if it turned out that the actual number of heads was 280, we would strongly believe that the coin was not fair, i.e., it was loaded.

EXAMPLE 13.7 Find the h-parameters of Fig. 13-9. This is the simple model of a bipolar junction transistor in its linear region of operation. By inspection, the terminal characteristics of Fig. 13-9 are V1 50I1 and I2 300I1 24

4.19. A die is tossed 120 times. Find the probability that the face 4 will turn up (a) 18 times or less, (b) 14 times or less, assuming the die is fair.

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(a) We want the probability of the number of 4s being between 0 and 18. This is given exactly by a 120 1 18 5 102 ba b a b 2 6 18 a 120 1 17 5 103 ba b a b 6 6 17 c a 120 1 0 5 120 ba b a b 6 6 0

Customer Call 3:

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but since the labor involved in the computation is overwhelming, we use the normal approximation. Considering the data as continuous, it follows that 0 to 18 4s can be treated as 0.5 to 18.5 4s. Also, m np 1 120a b 6 20 and s !npq A (120) a 1 b a 5 b 6 6 4.08

CHAP. 13]

Then 0.5 in standard units Required probability 0.5 20 4.08 (area between z (area between z 0.5 0.1443 5.02. 18.5 in standard units 5.02 and z 0.37 0.37)

(area under normal curve between z 0 and z 0 and z 0.3557 5.02) 0.37)

The terminal characteristics of a two-port circuit may also be described by still another set of hybrid parameters given in (26). I1 g11 V1 g12 I2 V2 g21 V1 g22 I2 where the coe cients gij are called inverse hybrid or g-parameters.

(b) We proceed as in part (a), replacing 18 by 14. Then 0.5 in standard units Required probability 5.02 14.5 in standard units 14.5 20 4.08 5.02 and z 1.35 1.35)

EXAMPLE 13.8 Find the g-parameters in the circuit shown in Fig. 13-10.

(area under normal curve between z (area between z (area between z 0.5 0.4115 0 and z 0 and z 0.0885 5.02) 1.35)

Customer calls about availability on a speci ed date. Sue brings up calendar for that week. There is a vacancy. Sue quotes a price. Sue gets name, address, telephone number, and credit card number. Sue enters information. Customer guarantees reservation. Reserve by date passes. Another customer requests that date. Nonguaranteed reservation is removed. 8. Write scenarios for the dental o ce problem (Problem 4.2). 1 Normal A patient calls for an appointment. The patient s name is recognized by the system. The system suggests a time. The patient accepts that time, and the receptionist enters the appointment. Two days before the appointment, the receptionist gets a reminder list with the patient s name and phone number. The receptionist calls to remind the patient. The patient comes for the appointment. After the appointment, the dental assistant schedules the patient s next appointment. 2 New Patient A patient calls for an appointment. The patient s name is not recognized by the system. The patient must be entered into the patient records system. 3 Multiple Appointments A patient calls and wants to make 6-month appointments for the next 2 years. The receptionist enters his name into the system and, when it is accepted, enters the agreed upon appointments.

It follows that if we were to take repeated samples of 120 tosses of a die, a 4 should turn up 14 times or less in about one-tenth of these samples.

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