the star8.1.22-TEQuestion Helpe belows commoy positiv 16 minutes. Complete parts (a) through (e) below.from Me0.0Suppose a geyser has a mean time between eruptions of 65 minutes. Let the interval of time between the eruptions be normally distributed with standard deviation(a) What is the probability that a randomly selected time interval between eruptions is longer than 73 minutes?0.0The probability that a randomly selected time interval is longer than 73 minutes is approximately 0.3085.(Round to four decimal places as needed.)3983 0.0(b) What is the probability that a random sample of 6 time intervals between eruptions has a mean longer than 73 minutes?7926 0.01791 0.1The probability that the mean of a random sample of 6 time intervals is more than 73 minutes is approximately(Round to four decimal places as needed.)5542 0.19146 0.12575 0.25804 0.28814 0.21594 0.334134 0.336433 0.338493 0.34032 0.4(1,1)41924 0.443319 0.4MoreEnter your answer in the answer box and then click Check Answer.4452 0.4partsremainingClear AllCheck Answer4,789DEC13tvMacBook Air(3)

Given Information: Mean μ = 65 Standard deviation σ = 16 (a) To find the probability that a randomly selected time interval between eruptions is longer than 73 minutes: Z-score is a measure which tells how many standard deviations away, a data value is, from the mean. It is given by the formula: z=X-μσ Required probability is obtained as follows: PX>73=PX-μσ>73-6516=PZ>0.5=1-PZ<0.5=1-0.69146=0.30854 Using a standard normal table (area to the left), look up for z-score 0.5 i.e., 0.5 in the row and .00 along the column, the intersection of both values gives a probability of 0.69146. Then subtract the value from total probability 1, since we want the area to the right of z-score. Thus, probability that a randomly selected time interval between eruptions is longer than 73 minutes is 0.3085 (b) To find the probability that a random sample of 6 time intervals between eruptions has a mean longer than 73 minutes: Here, n = 6 If a sample of size nis drawn from a normal population with mean μ and standard deviation σ, then the sampling distribution of sample mean is approximately normally distributed with mean μx¯=μ=65 and standard deviation of σx¯=σn=166=6.531972647 Required probability is obtained as follows: PX¯>73=PX¯-μx¯σx¯>73-656.531972647=PZ>1.2247=1-PZ<1.2247=1-0.889656 [using excel function "=NORM.S.DIST(1.2247,TRUE)"]=0.110344 (or) using standard normal table, area to the left of z-score 1.22 is 0.88877 then subtract from 1 i.e., 0.11123. Thus, probability that a random sample of 6 time intervals between eruptions has a mean longer than 73 minutes is 0.1103

Math

Statistics

Suppose a geyser has a mean time between eruptions of 65 minutes. Let the interval of time between the eruptions be normally distributed with standard devia 16 minutes. Complete parts (a) through (e) below. (a) What is the probability that a randomly selected time interval between eruptions is longer than 73 minutes? The probability that a randomly selected time interval is longer than 73 minutes is approximately 0.3085. (Round to four decimal places as needed.) (b) What is the probability that a random sample of 6 time intervals between eruptions has a mean longer than 73 minutes? The probability that the mean of a random sample of 6 time intervals is more than 73 minutes is approximately.. (Round to four decimal places as needed.)

Suppose a geyser has a mean time between eruptions of 65 minutes. Let the interval of time between the eruptions be normally distributed with standard devia 16 minutes. Complete parts (a) through (e) below. (a) What is the probability that a randomly selected time interval between eruptions is longer than 73 minutes? The probability that a randomly selected time interval is longer than 73 minutes is approximately 0.3085. (Round to four decimal places as needed.) (b) What is the probability that a random sample of 6 time intervals between eruptions has a mean longer than 73 minutes? The probability that the mean of a random sample of 6 time intervals is more than 73 minutes is approximately.. (Round to four decimal places as needed.)

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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