S. Suppose that X has a Poisson distribution with h= 80. Find the probability P(X< 70) based on the corresponding Poisson distribution and approximate normal distribution. Is the normal approximation reasonable?
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- Assume the Poisson distribution applies. Use the given mean to find the indicated probability. Find P(6) when μ=6.Help me pleaseAssume Z has a standard normal distribution. Use Appendix Table III to determine the value for z that solves each of the following: (a) P(- z < Z < z) = 0.95. z = 1.96 (Round the answer to 2 decimal places.) (b) P(- z < Z < z) = 0.99. z = 2.576 (Round the answer to 2 decimal places.) (c) P(-z< Z < z) = 0.66. z = i (d) P(- z < Z < z) = 0.9973. z = (Round the answer to 2 decimal places.) (Round the answer to 1 decimal place.)
- Let x represent the dollar amount spend on supermarket impulse buying in a 10-minute unplanned shopping interval. The mean of this distribution is µ=$25 and the standard deviation is =$10. If we assume the x distribution is approximately normal: (1) What is the probability that a randomly selected shopper will spend between $18 and $22? (1) Consider a random sample of n = 100 shoppers. What is the probability that is between $18 and $22? (2) State two different ways we know the distribution from part (b) is normally distributed.Show complete solution and clear hand writing. Show illustration and provide its given data.Assume that we have two normal distributions both with means 0 and standard deviations σ1 and σ2. If σ1 ≥ σ2, then which of P (0 ≤ x ≤ σ1) and P (0 ≤ x ≤ σ2) is bigger? Explain your answer.
- Assume the random variable X is normally distributed with mean μ=50 and standard deviation σ=7. Compute the probability. Be sure to draw a normal curve with the area corresponding to the probability shaded. P(X>36) Which of the following normal curves corresponds to P(X>36)? A. 36 50 A normal curve has a horizontal axis with two labeled coordinates, 36 and 50. The curve's peak is near the top of the graph at horizontal coordinate 50. Two vertical line segments run from the horizontal axis to the curve at horizontal coordinates 36 and 50. The area under the curve between the vertical line segments is shaded. B. 36 50 A normal curve has a horizontal axis with two labeled coordinates, 36 and 50. The curve's peak is near the top of the graph at horizontal coordinate 50. Two vertical line segments run from the horizontal axis to the curve at horizontal coordinates 36 and 50. The area…SHOW ALL WORKShow complete and clear (if it is hand writing) solution and also provide given and illustration if possible. Thank you. explain your answer
- Los Angeles workers have an average commute of 31 minutes. Suppose the LA commute time is normally distributed with a standard deviation of 14 minutes. Let X represent the commute time for a randomly selected LA worker.a. What is the distribution of X? X ~ N(,)b. Find the probability that a randomly selected LA worker has a commute that is longer than 35 minutes. Round to 4 decimal places. c. Find the 75th percentile for the commute time of LA workers. Round to 2 decimal places. minutesThe number of hours per week that the television is turned on is determined for each family in a sample. The mean of the data is 31 hours and the median is 27.2hours. Twenty-four of the families in the sample turned on the television for 16 hours or less for the week. The 8th percentile of the data is 16 hours. Based on the given information, determine if the following statement is true or false. The first quartile is less than 16 hours.An elevator can safely hold 3500 pounds. A sign in the elevator limits the passenger count to 15. If the adult population has a mean weight of 180 pounds with a 25-pound standard deviation, how unusual would it be, if the central limit theorem applied, that an elevator holding 15 people would be carrying more than 3500 pounds? Note. Use pnorm which is the normal distribution function of R.