### STAT Mutiple Choice Question Complete Solution

Question Details: #1288
STAT Mutiple Choice Question Complete Solution

 Find the following probabilities based on a standard normal variable Z. Use Table 1. (Round your answers to 4 decimal places.)

 a. P(Z > 0.74) b. P(Z ≤ −1.92) c. P(0 ≤ Z ≤ 1.62) d. P(−0.90 ≤ Z ≤ 2.94)

 The cumulative probabilities for a continuous random variable X are P(X ≤ 10) = 0.42 and P(X ≤ 20) = 0.66. Calculate the following probabilities. (Round your answers to 2 decimal places.)

 a. P(X > 10) b. P(X > 20) c. P(10 < X < 20)

 Let X be normally distributed with mean μ = 120 and standard deviation σ = 20. Use Table 1.

 a. Find P(X ≤ 86). (Round "z" value to 2 decimal places and final answer to 4 decimal places.)

 P(X ≤ 86)

 b. Find P(80 ≤ X ≤ 100). (Round "z" value to 2 decimal places and final answer to 4 decimal places.)

 P(80 ≤ X ≤ 100)

 c. Find x such that P(X ≤ x) = 0.40. (Round "z" value to 2 decimal places and final answer to nearest whole number.)

 x

 d. Find x such that P(X > x) = 0.90. (Round "z" value to 2 decimal places and final answer to 1 decimal place.)

 x

 Let X be normally distributed with mean μ = 2.5 and standard deviation σ = 2. Use Table 1.

 a. Find P(X > 7.6). (Round "z" value to 2 decimal places and final answer to 4 decimal places.)

 P(X > 7.6)

 b. Find P(7.4 ≤ X ≤ 10.6). (Round "z" value to 2 decimal places and final answer to 4 decimal places.)

 P(7.4 ≤ X ≤ 10.6)

 c. Find x such that P(X > x) = 0.025. (Round "z" value and final answer to 2 decimal places.)

 x

 d. Find x such that P(x ≤ X ≤ 2.5) = 0.4943. (Negative value should be indicated by a minus sign. Round "z" value and final answer to 2 decimal places.)

 x

 Find the following z values for the standard normal variable Z. Use Table 1. (Negative values should be indicated by a minus sign. Round your answers to 2 decimal places.)

 a. P(Z ≤ z) = 0.9744 b. P(Z > z) = 0.8389 c. P(−z ≤ Z ≤ z) = 0.95 d. P(0 ≤ Z ≤ z) = 0.3315

Exhibit 6-1. You are planning a May camping trip to Denali National Park in Alaska and want to make sure your sleeping bag is warm enough. The average low temperature in the park for May follows a normal distribution with a mean of 32°F and a standard deviation of 8°F.

Refer to Exhibit 6-1. One sleeping bag you are considering advertises that it is good for temperatures down to 25°F. What is the probability that this bag will be warm enough on a randomly selected May night at the park?

 0.88 0.8106 0.1894 0.3106

It is known that the length of a certain product X is normally distributed with μ = 20 inches. How is the probability related to ?

 \ is the same as \. \ is smaller than \. No comparison can be made with the given information. \ is greater than \.

Let X be normally distributed with mean μ and standard deviation σ > 0. Which of the following is true about the z value corresponding to a given x value?

 A positive z = (x - μ)/σ indicates how many standard deviations x is above μ. All of the above. A negative z = (x - μ)/σ indicates how many standard deviations x is below μ. The z value corresponding to x = μ is zero.

Find the probability P(-1.96 ≤ Z ≤ 0).

 0.025 0.475 0.525 0.05

The probability that a normal random variable is less than its mean is ___.

 1.0 Cannot be determined 0.0 0.5

How many parameters are needed to fully describe any normal distribution?

 2 1 3 4

The time to complete the construction of a soapbox derby car is normally distributed with a mean of three hours and a standard deviation of one hour. Find the probability that it would take between 2.5 and 3.5 hours to construct a soapbox derby car.

 0.3085 0.617 0.383 0.6915

Let X be normally distributed with mean µ = 250 and standard deviation σ = 80. Find the value x such that P(X ≤ x) = 0.9394.

 126 1.55 374 -1.55

Exhibit 6-2. Gold miners in Alaska have found, on average, 12 ounces of gold per 1000 tons of dirt excavated with a standard deviation of 3 ounces. Assume the amount of gold found per 1000 tons of dirt is normally distributed.

Refer to Exhibit 6-2. What is the probability the miners find more than 16 ounces of gold in the next 1000 tons of dirt excavated?

 0.5918 0.0918 0.9082 0.4082

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If X has a normal distribution with   and   , then the probability   can be expressed in terms of a standard normal variable Z as _______.

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Solution Details: #1266
STAT Mutiple Choice Question Complete Solution

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