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Nimfa-mama [501]
3 years ago
7

Find the 15th term of the arithmetic sequence if a1 = -3 and d = 2

Mathematics
1 answer:
pantera1 [17]3 years ago
3 0

Answer:

25

Step-by-step explanation:

a1 = - 3               Given

d = 2                   Given

n = 15                  Given

Formula

tn = a1 + (n - 1) * d

Substitute and solve

t15 = -3 + (15 - 1) * 2               Calculate what's in the brackets.

t15 = -3 + 14*2                        Combne

t15 = -3 + 28                          Add the two terms

t15 = 25


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Complete question:

He amount of time that a customer spends waiting at an airport check-in counter is a random variable with mean 8.3 minutes and standard deviation 1.4 minutes. Suppose that a random sample of n equals 47 customers is observed. Find the probability that the average time waiting in line for these customers is

a) less than 8 minutes

b) between 8 and 9 minutes

c) less than 7.5 minutes

Answer:

a) 0.0708

b) 0.9291

c) 0.0000

Step-by-step explanation:

Given:

n = 47

u = 8.3 mins

s.d = 1.4 mins

a) Less than 8 minutes:

P(X

P(X' < 8) = P(Z< - 1.47)

Using the normal distribution table:

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b) between 8 and 9 minutes:

P(8< X' <9) =[\frac{8-8.3}{1.4/ \sqrt{47}}< \frac{X'-u}{s.d/ \sqrt{n}} < \frac{9-8.3}{1.4/ \sqrt{47}}]

= P(-1.47 <Z< 6.366)

= P( Z< 6.366) - P(Z< -1.47)

Using normal distribution table,

NORMSDIST(6.366)-NORMSDIST(-1.47)

0.9999 - 0.0708

= 0.9291

c) Less than 7.5 minutes:

P(X'<7.5) = P [Z< \frac{7.5-8.3}{1.4/ \sqrt{47}}]

P(X' < 7.5) = P(Z< -3.92)

NORMSDIST (-3.92)

= 0.0000

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3 years ago
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