Welcome to Westonci.ca, the ultimate question and answer platform. Get expert answers to your questions quickly and accurately. Our platform provides a seamless experience for finding precise answers from a network of experienced professionals. Explore comprehensive solutions to your questions from a wide range of professionals on our user-friendly platform.
Sagot :
To determine the probability [tex]\( P(x \geq 92) \)[/tex] for a normal distribution with a mean [tex]\(\mu = 98\)[/tex] and a standard deviation [tex]\(\sigma = 6\)[/tex], follow these steps:
1. Calculate the z-score for [tex]\( x = 92 \)[/tex]:
The z-score formula is given by:
[tex]\[ z = \frac{x - \mu}{\sigma} \][/tex]
Substitute [tex]\( x = 92 \)[/tex], [tex]\( \mu = 98 \)[/tex], and [tex]\( \sigma = 6 \)[/tex] into the formula:
[tex]\[ z = \frac{92 - 98}{6} = \frac{-6}{6} = -1.0 \][/tex]
2. Find the cumulative probability for the calculated z-score:
The cumulative probability for a z-score can be obtained from standard normal distribution tables or using statistical software. For [tex]\( z = -1.0 \)[/tex], the cumulative probability [tex]\( P(Z < -1.0) \)[/tex] is approximately:
[tex]\[ P(Z < -1.0) \approx 0.1587 \][/tex]
This is the probability that a randomly selected value from this distribution is less than 92.
3. Determine the probability [tex]\( P(x \geq 92) \)[/tex]:
To find the probability that [tex]\( x \)[/tex] is greater than or equal to 92, use the complement rule:
[tex]\[ P(x \geq 92) = 1 - P(x < 92) \][/tex]
Substitute the cumulative probability found in the previous step:
[tex]\[ P(x \geq 92) = 1 - 0.1587 \approx 0.8413 \][/tex]
Therefore, the probability [tex]\( P(x \geq 92) \)[/tex] is approximately 0.8413.
Hence, the correct answer is:
C. 0.84
1. Calculate the z-score for [tex]\( x = 92 \)[/tex]:
The z-score formula is given by:
[tex]\[ z = \frac{x - \mu}{\sigma} \][/tex]
Substitute [tex]\( x = 92 \)[/tex], [tex]\( \mu = 98 \)[/tex], and [tex]\( \sigma = 6 \)[/tex] into the formula:
[tex]\[ z = \frac{92 - 98}{6} = \frac{-6}{6} = -1.0 \][/tex]
2. Find the cumulative probability for the calculated z-score:
The cumulative probability for a z-score can be obtained from standard normal distribution tables or using statistical software. For [tex]\( z = -1.0 \)[/tex], the cumulative probability [tex]\( P(Z < -1.0) \)[/tex] is approximately:
[tex]\[ P(Z < -1.0) \approx 0.1587 \][/tex]
This is the probability that a randomly selected value from this distribution is less than 92.
3. Determine the probability [tex]\( P(x \geq 92) \)[/tex]:
To find the probability that [tex]\( x \)[/tex] is greater than or equal to 92, use the complement rule:
[tex]\[ P(x \geq 92) = 1 - P(x < 92) \][/tex]
Substitute the cumulative probability found in the previous step:
[tex]\[ P(x \geq 92) = 1 - 0.1587 \approx 0.8413 \][/tex]
Therefore, the probability [tex]\( P(x \geq 92) \)[/tex] is approximately 0.8413.
Hence, the correct answer is:
C. 0.84
Thanks for using our service. We aim to provide the most accurate answers for all your queries. Visit us again for more insights. We appreciate your visit. Our platform is always here to offer accurate and reliable answers. Return anytime. Keep exploring Westonci.ca for more insightful answers to your questions. We're here to help.