Let x be a continuous random variable with a standard normal distribution. Using the accompanying standard normal distribution​ table, find   Use the table attached below ​P(−1.71 <= x <= 1.39) =    (round to four decimal places if needed)

Central High School believes their students have unusually high SAT scores on average. The school has 165 students.Based on national data, the average SAT score is 1067 with a population standard deviation of 207. Assume SAT scores are normally distributed. Let X be the random variable representing the mean SAT scores for groups of 165 randomly selected students.a. Fill in the blank, rounding your answers to 2 decimal places if needed. According to the Central Limit Theorem, X is approximately normal with a mean of  and a standard error of the mean  .b. Find the z-score associated to a sample with a mean of 1109, using the sampling distribution. Round your answer to two decimal places. c. Find the probability that a randomly selected sample of 165 students has a mean SAT score higher than 1109. Round your answer to 4 decimal places. d. Central High School finds that for their students, the average SAT score is 1109. Are they justified in saying their students perform unusually well on…

Assume that x has a normal distribution with the specified mean and standard deviation. Find the indicated probability. (Round your answer to four decimal places.) A USE SALT l = 106; o = 13 P(x z 120) =

Use the table of areas under the standard normal curve to find the probability that a z-score from the standard normal distribution will lie within the interval. (Round your answer to four decimal places.) z < 1.3

Assume that adults have IQ scores that are normally distributed with a mean of μ= 100 and a standard deviation σ = 20. Find the probability that a randomly selected adult has an IQ less than 120. Click to view page 1 of the table. Click to view page 2 of the table. The probability that a randomly selected a (Type an integer or decimal rounded to fo Standard Normal Table (Page 1) NEGATIVE z Scores Standard Normal (z) Distribution: Cumulative Area from the LEFT .00 .01 02 .03 .04 .05 .06 .07 .08 .09 -3.50 and lower .0001 -3.4 .0003 .0003 .0003 .0003 .0003 .0003 .0003 .0003 .0003 0002 -3.3 .0005 .0005 .0005 .0004 .0004 .0004 0004 .0004 0004 .0003 -3.2 .0007 .0007 .0006 .0006 .0006 .0006 0006 .0005 .0005 0005 -31 0010 .0009 .0009 .0009 .0008 .0008 .0008 .0008 .0007 .0007 -3.0 .0013 0013 .0013 0012 .0012 .0011 .0011 .0011 0010 0010 -2.9 .0019 .0018 0018 .0017 .0016 .0016 0015 .0015 .0014 .0014 -2.8 .0026 .0025 .0024 .0023 .0023 .0022 .0021 .0021 .0020 0019 -2.7 .0035 .0034 .0033 .0032 .0031…

Let z be a random variable with a standard normal distribution. Find the indicated probability. (Round your answer to four decimal places.)   P(z ≥ −1.60)= _______________Shade the corresponding area under the standard normal curve.

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.