Bsm 1 2 3 B, Read and answer the following problems with random samples taken from the normal population.Show all the necessary solutions.1. Theaverage onlineteacher's salaryperhour is P380.00withastandarddeviationof P51.00. Forssample of 75 online teachers, what is the probability that the sample mean is greater thanP400.002. The national average percentage score of Grade 6 in National Achievement Test (NAT) recenulfor Math subject is 36.66 with a standard deviation of 3.57. Ifa random sample of 200 scores wselected, what is the probability that the sample average percentage score is higher than 453. The number of hours spent playing mobile legends a day by teenagers has a mean of 8 hourwith a standard deviation of 3.5 hours. Find the probability that if you select 50 randomteenagers, the mean number of hours a day spent playing games is between 5 and 7.5 hours4. Kyle has a collection of more than 300 songs in his phone that has a mean duration of 2.75minutes and a standard deviation of 0.6 minutes. Suppose that every week he makes aplaylist by taking random sample of 36 of these songs, calculate the sample mean durationof the songs and the standard error of the sampling distribution of the sample means.5. On the average, basketball players drink 2.3 liters of water with a standard deviationof 0.9 liter during a game. If the team manager asks his assistant to bring 45 litersof water for 15 players, what is the probability that they will run out of water?6. Suppose that students who finished JHS in a public school get an average of 5.6 hours of sleepeach night with a standard deviation of 1.7 hours. What is the probability that a random selectedgroup of 35 public school students get more than 6 hours of sleep, on the average each night?7. The average life of a smartphone is 7 years with a standard deviation of 1 year. Assumingthat the lives of these phones follow approximately a normal distribution, find the probabilitythat the mean life of a random sample of 9 smartphones fall between 6.4 and 7.2 years.8. Given a normal random variable X with a mean of 20, a variance of 9, and a random sample of ntakenfrom the distribution, whatsamplesize (n)isnecessaryinorderthat P(19.9< X <20.1)=0.95?ba Je o n ge.dtagoy lmon sdi l.dat s via9. Suppose that systolic blood pressures of a certain population are normally distributed with amean of 120, a standard deviation of 4, and a sample size 28 is taken from this population,what is the probability that a single sample will have a mean blood pressure of less than 125?ssda alqmsa ads10. Study reports that the average person uses 120 liters of water daily. If the standard deviationis 20 liters, find the probability that the mean of randomly selected sample of 15 people will bebetween 120 and 125 liters.

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population B. Read and answer the following problems with random samples taken from Show all the necessary solutions. 1. Theaverage onlineteacher's salaryperhour is P380.00withastandarddeviation of P51.00. Fors sample of 75 online teachers, what is the probability thatthe sample meanis greater than P400.00 2. The national average percentage score of Grade 6 in National Achievement Test (NAT) recend for Math subject is 36.66 with a standard deviation of 3.57. Ifa random sample of 200 scores w selected, what is the probability that the sample average percentage score is higher than 45