Question

The reading speed of second grade students in a large city is approximately​ normal, with a mean of 88 words per minute​ (wpm) and a standard deviation of 10 wpm. Complete parts​ (a) through​ (f). What is the probability a randomly selected student in the city will read more than 92 words per​ minute?

Answer 1

To calculate the probability that a randomly selected student in the city will read more than 92 words per minute, we need to use the standard normal distribution. The probability is approximately 0.3446 or 34.46%.

Step-by-step explanation:

To calculate the probability that a randomly selected student in the city will read more than 92 words per minute, we need to use the standard normal distribution. First, we need to convert the raw score of 92 to a z-score using the formula:

1. z = (x - μ) / σ

where x is the raw score, μ is the mean, and σ is the standard deviation. Plugging in the values:

1. z = (92 - 88) / 10 = 0.4

Next, we need to find the area to the right of the z-score of 0.4 on the standard normal distribution. This can be done using a z-table or a calculator. The probability can be interpreted as the percentage of students who read more than 92 words per minute, so we need to find the area to the right of 0.4:

1. probability = 1 - P(z < 0.4)

This probability can be found using a z-table or a calculator, and it is approximately 0.3446 or 34.46%.