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sergey [27]
3 years ago
14

Willow Brook National Bank operates a drive-up teller window that allows customers to complete bank transactions without getting

out of their cars. On weekday mornings, arrivals to the drive-up teller window occur at random, with an arrival rate of 24 customers per hour or 0.4 customers per minute.
(a) What is the mean or expected number of customers that will arrive in a five-minute period?
(b) Use the arrival rate in part (a) and compute the probabilities that exactly 0, 1, 2, and 3 customers will arrive during a five-minute period. If required, round your answers to four decimal places.
(c) Delays are expected if more than three customers arrive during any five-minute period. What is the probability that delays will occur? If required, round your answer to four decimal places.
Mathematics
1 answer:
luda_lava [24]3 years ago
5 0

Answer:

2, 0.135, 0.270, 0.270, 0.180, 0.145

Step-by-step explanation:

1. To calculate the mean of people arriving in 5 minute period:

We know the arrival rate of minute is 0.4, so people arriving in 5 minutes will be

0.4 x 5 = 2

2. From part 1 it is known thay mean arrival time=2

For this we will use poisson's probability formula that is

P(X=x) = (2^x) x Exp^(-2/x!)

For X=0

P(X=0) = (2^0) x Exp^(-2/0!) = 0.135

For X = 1

P(X=1) = (2^1) x Exp^(-2/1!) = 0.270

For X = 2

P(X=2) = (2^2) x Exp^(-2/2!) = 0.270

For X = 3

P(X=3) = (2^3) x Exp^(-2/3!) = 0.180

3. For delay expected if more than 3 customer arrive in 5 minutes.

P(X>3) = 1 - P(X=0) - P(X=1) - P(X=2) - P(X=3)

P(X>3) = 1-0.135-0.270-0.270-0.180

P(X>3) = 0.145

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3 years ago
If a basketball player made 72 out of 85 free throws attempts how many could she make in 200 attempts
DedPeter [7]

Answer:

169

Step-by-step explanation:

Use a proportion:

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2 years ago
An instructor who taught two sections of engineering probability last term, the first with 20 students and thesecond with 30, de
Oliga [24]

Answer:

0.207

Step-by-step explanation:

This is an hypergeometric distribution problem

An hypergeometric distribution has the same sense as the discrete probabilities of binomial distribution, but unlike binomial distribution, hypergeometric distribution does not allow replacement.

Binomial distribution expresses the probability of picking k objects from n with replacement, but hypergeometric distribution expresses picking k objects from n without replacement, with the finite total population, N, containing K objects.

It is expressed mathematically as

h(k: n, K, N) = (ᴷCₖ)(ᴺ⁻ᴷCₙ₋ₖ)/(ᴺCₙ)

where

k = number of students in the 2nd section required to be in the first 15 graded projects (number of successes) = 10

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h(10: 15, 30, 50) = (³⁰C₁₀)(²⁰C₅)/(⁵⁰C₁₅)

= (30,045,015)(15,504)/(2,250,829,575,120)

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