Chp 6 Quiz STA 2023 McGraw Hill

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 more than five hours to construct a soapbox derby car.

0.0228 The normal transformation implies that any value x of X has a corresponding value z of Z given by 2formula69.mml Compute P(X > 5).

Suppose the life of a particular brand of laptop battery is normally distributed with a mean of 8 hours and a standard deviation of 0.6 hours. What is the probability that the battery will last more than 9 hours before running out of power?

0.0475 The normal transformation implies that any value x of X has a corresponding value z of Z given by formula88.mml Compute P(X > 9). Note that P(Z > z) = 1 - P(Z < z).

Gold miners in Alaska have found, on average, 12 ounces of gold per 1,000 tons of dirt excavated with a standard deviation of 3 ounces. Assume the amount of gold found per 1,000 tons of dirt is normally distributed. What is the probability the miners find more than 16 ounces of gold in the next 1,000 tons of dirt excavated?

0.0918 The normal transformation implies that any value x of X has a corresponding value z of Z given by 2formula83.mml Compute P(X > 16). Note that P(Z ≥ z) = 1 - P(Z < z).

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

0.4750 Use z table that provides cumulative probabilities P(Z ≤ z) for positive and negative values of z. Compute P(z1 ≤ Z ≤ z2) = P(Z ≤ z2) - P(Z ≤ z1).

Gold miners in Alaska have found, on average, 12 ounces of gold per 1,000 tons of dirt excavated with a standard deviation of 3 ounces. Assume the amount of gold found per 1,000 tons of dirt is normally distributed. What is the probability the miners find between 10 and 14 ounces of gold in the next 1,000 tons of dirt excavated?

0.4972 The normal transformation implies that any value x of X has a corresponding value z of Z given by formula85.mml Compute P(10 ≤ X ≤ 14). Note that P(z1 ≤ Z ≤ z2) = P(Z ≤ z2)1 - P(Z ≤ z1).

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. An inexpensive bag you are considering advertises to be good for temperatures down to 38°F. What is the probability that the bag will not be warm enough?

0.7734 The normal transformation implies that any value x of X has a corresponding value z of Z given by formula81.mml Compute P(X > 38). Note that P(Z ≥ z) = 1 - P(Z < z).

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. 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?

0.8106 The normal transformation implies that any value x of X has a corresponding value z of Z given by formula79.mml Compute P(X ≥ 25). Note that P(Z ≥ z) = 1 - P(Z < z).

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

0.9500 Use z table that provides cumulative probabilities P(Z ≤ z) for positive and negative values of z. Compute P(z1 ≤ Z ≤ z2) = P(Z ≤ z2) - P(Z ≤ z1).

For any normally distributed random variable with mean μ and standard deviation σ, the percent of the observations that fall between [μ - 2σ, μ + 2σ] is the closest to _______.

95.44% The empirical rule states that P(μ - 2σ ≤ X ≤ μ + 2σ) = 0.9544.

The probability density function for a continuous uniform distribution is positive for all values between -∞ and +∞.

False The uniform distribution is defined on a bounded interval, denoted by [a, b].

It is known that the length of a certain product X is normally distributed with μ = 20 inches. How is the probability P(X < 20) related to P(X < 16)?

P(X < 20) is greater than P(X < 16). The normal distribution is symmetric around its mean: P(X < μ) = P(X > μ) = 0.5. If x < μ then P(X < x) < 0.5 and P(X < μ) > P(X < x).

It is known that the length of a certain product X is normally distributed with μ = 20 inches. How is the probability P(X > 16) related to P(X < 16)?

P(X > 16) is greater than P(X < 16). The normal distribution is symmetric around its mean: P(X < μ) = P(X > μ) = 0.5. If x < μ then P(X < x) < 0.5 and P(X > x) > 0.5.

The probability density function of a continuous random variable is the counterpart to the probability mass function of a discrete random variable.

True The area under any probability density function is 1, and as for any discrete random variable X with values x1, x2, x3, . . . , xn, formula152.mml.