A bank has kept records of the checking balances of its customers and determined that the average daily balance of its customers is $413 with a standard deviation of $68. A random sample of 61 checking accounts is selected. What is the probability that the sample mean will be between $402.6 and $410.4?

1 answer

Question:

A bank has kept records of the checking balances of its customers and determined that the average daily balance of its customers is $413 with a standard deviation of $68. A random sample of 61 checking accounts is selected. What is the probability that the sample mean will be between $402.6 and $410.4?

Answer:Probability that the sample mean will be between $402.6 and $410.4 is 0.2689.Step-by-step explanation:We are given that a bank has kept records of the checking balances of its customers and determined that the average daily balance of its customers is $413 with a standard deviation of $68.A random sample of 61 checking accounts is selected.Let [tex]\bar X[/tex] = sample meanNow, the z score probability distribution for sample mean is given by; Z = [tex]\frac{\bar X-\mu}{\frac{\sigma}{\sqrt{n} } }[/tex] ~ N(0,1)where, [tex]\mu[/tex] = average daily balance of its customers = $413 [tex]\sigma[/tex] = standard deviation = $68 n = sample of checking accounts = 61So, probability that the sample mean will be between $402.6 and $410.4 is given by = P($402.6 < [tex]\bar X[/tex] < $410.4) = P([tex]\bar X[/tex] < $410.4) - P([tex]\bar X[/tex] [tex]\leq[/tex] 402.6)P([tex]\bar X[/tex] < $410.4) = P( [tex]\frac{\bar X-\mu}{\frac{\sigma}{\sqrt{n} } }[/tex] < [tex]\frac{410.4-413}{\frac{68}{\sqrt{61} } }[/tex] ) = P(Z < -0.29) = 1 - P(Z [tex]\leq[/tex] 0.29) = 1 - 0.61409 = 0.38591 P([tex]\bar X[/tex] [tex]\leq[/tex] $402.6) = P( [tex]\frac{\bar X-\mu}{\frac{\sigma}{\sqrt{n} } }[/tex] [tex]\leq[/tex] [tex]\frac{402.6-413}{\frac{68}{\sqrt{61} } }[/tex] ) = P(Z [tex]\leq[/tex] -1.19) = 1 - P(Z < 1.19) = 1 - 0.88298 = 0.11702Therefore, P($402.6 < [tex]\bar X[/tex] < $410.4) = 0.38591 - 0.11702 = 0.2689Hence, probability that the sample mean will be between $402.6 and $410.4 is 0.2689.

2
Select the correct answer.
Which description best defines the central idea of an informational text?
A the analysis of the details the author provides
B.
the main point the author is trying to make
C. the examples that an author uses throughout the text
D. the supporting evidence an author cites
R...

Which of the following mutations would be most likely to have a harmful effect on an organism? (1 point)
o all mutations have a harmful effect on organisms
O a deletion of 3 bases near the center of a gene
a substitution of a thymine for an adenine
o there is not enough information to know whether a...

For questions 19-21 select the groups of words which are sentences.
19. (a) Across the river
(b) We were all together at the ball game
(C) On top of
(d) with a light heart
20. (a) Will we see you tomorrow?
(b) At the shop
(c) In the yard
(d) Over and under it
21. (a) All the girls wore red yesterday...

Hans removed 90 fish from his pond over a period of 9 days. He removed the same number of fish each day. What was the change in the number of fish in the pond each day?
Tell me...