2.85 (b) Find the probability that the interest rate paid by a financial institution chosen at random is less than 2.56% per year
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The interest rates paid by 30 financial institutions on a certain day for money market deposit accounts are shown in the accompanying table.
| Rate % | 2 | 2.25 | 2.55 | 2.56 | 2.58 | 2.60 | 2.65 | 2.85 |
|---|---|---|---|---|---|---|---|---|
| Institutions | 1 | 8 | 8 | 2 | 2 | 7 | 1 | 1 |
Let the random variable X denote the interest rate per year paid by a randomly chosen financial institution on its money market deposit accounts.
| Rate % |
P(X = x)
|
|
|---|---|---|
| 2 | ||
| 2.25 | ||
| 2.55 | ||
| 2.56 | ||
| 2.58 | ||
| 2.60 | ||
| 2.65 | ||
| 2.85 |
(b) Find the probability that the interest rate paid by a financial institution chosen at random is less than 2.56% per year. (Round your answer to three decimal places.)
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- What would this normal probability plot lead you to believe about the normality of the population from which the data were taken? 2.0 1.0 -1.0 -2.0 120 130 140 150 160 170 180 190 The points show a pattern straying from a straight line, indicating that the population is not approximately normal. The points appear to be randomly scattered, indicating that the population is probably approximately normally distributed. The points roughly follow a linear pattern, indicating that the population is probably approximately normally distributed. The points roughly follow a linear pattern, indicating that the population is probably not approximately normally distributed. z-ScoreYorkies Company has fixed costs of $80,000 per month. Variable costs are $12 per item produced. The selling price per unit is fixed at $20. From the past company data, you have determined that Yorkies Company's monthly output follows a normal probability distribution with mean 11,100 and variance 550,000 . Calculate the chance that Yorkies will make a loss this month. a.11% b.10% c.9% d.7% e.7%Condom Failure Rate: According to the Department of Health and Human Services, the failure rate for male condoms is 18%. The accompanying table is based on the failure rate of 18%, where x represents the number of condoms that fail when six are tested. x P(x) 0 0.304 1 0.400 2 0.220 3 0.064 4 0.011 5 0.001 6 0+ Does the table describe a probability distribution? Why or Why not? Assuming that the table does describe a probability distribution, find its mean? Assuming that the table does describe a probability distribution, find its standard deviation? If 6 condoms are tested and 5 of them fail, is 5 a significantly high number of failures? Why or Why not? What does the symbol 0+ represent?
- You buy a stock that has an annual expected return of 20% and a standard deviation of 25%. Last year, investors in the stock lost 32.5% of their money and the year before they gained 40%. What is the probability that the outcome on this stock will be better than -32.5%, but less than +40% this year? a 18.75% b. 52.50% c. 78.82% d. 22.97% e. 77.03%Historical data show that customers who download music from a popular Web service spend approximately $24 per month, with a standard deviation of $4. Assume the spending follows the normal probability distribution. Find the probability that a customer will spend at least $20 per month. How much (or more) do the top 7% of customers spend? What is the probability that a customer will spend at least $20 per month?A probability distribution for various prize values is given by the following table. Prizes Probabilities $0.00 0.82 $100.00 0.11 $500.00 0.06 $10,000.00 0.01 Find the expected value of a prize. Round your answer to two decimal places.
- Relax! A recent survey asked 1682 people how many hours per day they were able to relax. The results are presented in the following table. Number of Hours Frequency 0 113 1 184 2 336 3 251 4 318 5 234 6 151 7 35 8 60 Total 1682 Send data to Excel Consider these 1682 people to be a population. Let X be the number of hours of relaxation for a person sampled at random from this population. Part 1 of 5 (a) Construct the probability distribution of X . Round the answer to three decimal places. x 0 1 2 3 4 5 6 7 8 P ( x ) Part 2 of 5 (b) Find the probability that a person relaxes more than 4 hours per day. The probability that a person relaxes more than 4 hours per day is…Historical data show that customers who download music from a popular Web service spend approximately $22 per month, with a standard deviation of $3. Assume the spending follows the normal probability distribution. Find the probability that a customer will spend at least $19 per month. How much (or more) do the top 9% of customers spend? What is the probability that a customer will spend at least $19 per month? (Round to four decimal places as needed.) How much do the top 9% of customers spend? (Round to the nearest cent as needed.)British Travel Agency has asked a junior manager to investigate flight delays during the week before Christmas at Heathrow Airport. The random variable X is the number of flights delayed per hour. The results are shown in the following table. x 0 1 5 2 3 4 6 7 8. p(x) 0.10 0.08 0.07 0.15 0.12 0.08 0.10 0.12 0.08 0.10 a) Show that the probability distribution is well defined and derive the cumulative probability distribution. b) Find the probability that there would be three through seven (inclusive) delayed flights per hour? c) Find the mean and variance of flights delayed per hour.
