Consider a standard normal random variable with = 0 and standard deviation = 1.
ID: 3361237 • Letter: C
Question
Consider a standard normal random variable with = 0 and standard deviation = 1. Use the table of Areas under the Normal Curve to find the following probabilities. (Enter your answers to four decimal places.)
(a) P(z < 1) =
(b) P(z > 1.16) =
(c) P(2.38 < z < 2.38) =
(d) P(z < 1.88) =
2.Find the following probabilities for the standard normal random variable z. (Round your answers to four decimal places.)
(a) P(1.47 < z < 0.65) =
(b) P(0.52 < z < 1.74) =
(c) P(1.56 < z < 0.48) =
(d) P(z > 1.36) =
(e) P(z < 4.39) =
(a) Find a z0 such that
3.P(z > z0) = 0.0262. (Round your answer to two decimal places.)
z0 =
(b) Find a z0 such that P(z < z0) = 0.8869. (Round your answer to two decimal places.)
z0 =
4.(a) Find a z0 that has area 0.9357 to its left. (Round your answer to two decimal places.)
z0 =
(b) Find a z0 that has area 0.08 to its left. (Round your answer to two decimal places.)
z0 =
5.Find the following percentiles for the standard normal random variable z. (Round your answers to two decimal places.)
(a) 90th percentile z =
(b) 92nd percentile z =
(c) 96th percentile z =
(d) 99th percentile z =
6.A normal random variable x has mean = 1.5 and standard deviation = 0.13. Find the probability associated with each of the following intervals. (Round your answers to four decimal places.)
(a) 1.00 < x < 1.30
(b) x > 1.35
(c) 1.35 < x < 1.60
7. An experimenter publishing in the Annals of Botany investigated whether the stem diameters of the dicot sunflower would change depending on whether the plant was left to sway freely in the wind or was artificially supported. Suppose that the unsupported stem diameters at the base of a particular species of sunflower plant have a normal distribution with an average diameter of 35 millimeters (mm) and a standard deviation of 3 mm.
(a) What is the probability that a sunflower plant will have a basal diameter of more than 37 mm? (Round your answer to four decimal places.)
(b) If two sunflower plants are randomly selected, what is the probability that both plants will have a basal diameter of more than 37 mm? (Round your answer to four decimal places.)
(c) Within what limits would you expect the basal diameters to lie, with probability 0.95? (Round your answers to two decimal places.)
lower limit mm
upper limit mm
(d) What diameter represents the 80th percentile of the distribution of diameters? (Round your answer to two decimal places.)
______mm
Explanation / Answer
1 Solution:-
(a) P(z < 1) = 0.8413
(b) P(z > 1.16) = 1 P(Z < 1.16) = 1 0.877 = 0.123
(c) P(2.38 < z < 2.38) = 0.9826
(d) P(z < 1.88) = 0.9699
2 solution:-
(a) P(1.47 < z < 0.65) = 0.6714
(b) P(0.52 < z < 1.74) = 0.2606
(c) P(1.56 < z < 0.48) = 0.2562
(d) P(z > 1.36) = =1 P( Z < 1.36) = 1 0.9131 = 0.0869
(e) P(z < 4.39) = 0
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3)
a) P(z > z0) = 0.0262
z0 = 1.94
b) P(z < z0) = 0.8869
z0 = 1.21
4.
(a) P(z < z0) = 0.9357
z0 = 1.52
b) P(z < z0) = 0.08
z0 = -1.41
5.
(a) 90th percentile z = 1.65
(b) 92nd percentile z = 1.75
(c) 96th percentile z = 2.05
(d) 99th percentile z = 2.58
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6 )
a) P(1.00 < x < 1.30) = P(3.8461 < Z < 1.5385) = 0.0617
b) P(x > 1.35) = P ( Z>1.1538 )=P ( Z<1.1538 )=0.8749
c) P (1.35 < x < 1.60 ) = P (1.1538<Z<0.7692 )=0.6543