A variable is normally distributed with a mean of 120 and a standard deviation of 5. One score is randomly...

A variable is normally distributed with a mean of 120 and a standard deviation of 5. One score is randomly sampled. What is the probability it is above 127?

A group of students at a school takes a history test. The distribution is normal with a mean of 25, and a standard deviation of 4. (a) Everyone who scores in the top 30% of the distribution gets a certificate. What is the lowest score someone can get and still earn a certificate? (b) The top 5% of the scores get to compete in a statewide history contest. What is the lowest score someone can get and still go onto compete with the rest of the state?

Use the normal distribution to approximate the binomial distribution and find the probability of getting 15 to 18 heads out of 25 flips. Compare this to what you get when you calculate the probability using the binomial distribution. Write your answers out to four decimal places.

What is the median recovery time? a. 2.7 b. 5.3 c. 7.4 d. 2.1

Height and weight are two measurements used to track a child’s development. The World Health Organization measures child development by comparing the weights of children who are the same height and the same gender. In 2009, weights for all 80cm girls in the reference population had a mean µ=10.2kg and standard deviation σ=0.8kg. Weights are normally distributed. X~N (10.2, 0.8). Calculate the z-scores that correspond to the following weights and interpret them. a. 11 kg b. 7.9 kg c. 12.2 kg.