Using the Central Limit Theorem Answers

A course for a snail race has times that are skewed right with a mean of 5.18 minutes and a standard deviation of 2.34 minutes. If a random sample of 38 snails is selected, what is the probability that the mean race time is less than 4.3 minutes?

The total number of forks dropped by customers per day at a busy restaurant is multimodal with a mean of 24.5 and a standard deviation of 3.3. If a random sample of 80 days is selected, what is the probability that the mean number of forks dropped during those days will be more than 25?

Chris makes a smoothie for breakfast every day. When he makes smoothies with bananas, the distribution of calories is skewed right with a mean of 248.6 and a standard deviation of 39.1. His berry smoothies have a distribution of calories that is approximately Normal with a mean of 279.1 calories and a standard deviation of 60.8. Random samples of 35 of each type of smoothie are selected. What is the probability of the banana smoothies having fewer mean calories than the berry smoothies?

The times a musician spends performing a rock song and a country song are approximately Normally distributed. The rock song has a mean time of 133 seconds with a standard deviation of 3.5 seconds, and the country song has a mean time of 126 seconds with a standard deviation of 3.3 seconds. If the musician randomly selects 4 times the rock song is played and 3 times the country song is played, what is the probability that the mean time for the rock song is less than the mean time for the country song?

The monthly cost for cell phones for plan Amazing has a mean of $39.17 with a standard deviation of $13.58, while the monthly cost for plan Best has a mean cost of $41.16 with a standard deviation of $7.18. A random sample of 37 phones is selected from plan Amazing, and a random sample of 40 phones is selected from plan Best. What is the probability that the mean cost for plan Amazing will be more than the mean cost for plan Best?

The number of pieces of cat food in a one-cup scoop is approximately Normally distributed with a mean of 344 pieces and a standard deviation of 16 pieces. If a random sample of 28 scoops of cat food is selected, what is the probability that the mean number of pieces will be more than 350 pieces?

The heights of a species of plant are approximately Normally distributed, have a mean of 9.31 cm, and have a standard deviation of 0.55 cm. If 20 of the plants are randomly selected, what is the probability that the mean plant height is less than 9.5 cm?

The distribution of time spent brushing teeth for the 1,200 students in a school is multimodal with a mean of 43 seconds and a standard deviation of 8.99 seconds. If a random sample of 9 students is selected, is it appropriate to calculate the probability of the sample mean being less than 30 seconds using an approximately Normal model?

Latisha owns two spas, one in Pine township and the other in Adams township. Each spa offers a 30-minute face, head, and neck massage to reduce muscle tension. However, therapists first ask each patient questions about their type of tension and stop about five minutes before the end of the 30 minutes to have time to prepare for the next patient. The number of minutes each therapist massages the patients at both spas is approximately Normally distributed, with the Pine spa having a mean of 22.6 minutes and a standard deviation of 1.7 minutes and the Adams spa having a mean of 21.0 minutes and a standard deviation of 2.8 minutes. If Latisha randomly selects 8 massage times from Pine and 9 from Adams, what is the probability that the mean time for Pine is longer than the mean time for Adams?

The distribution of the number of blocks a young child can stack before their tower falls is approximately Normally distributed with a mean of 12.7 blocks and a standard deviation of 1.4 blocks. If 6 of the child’s towers are randomly selected, what is the probability that the mean number of blocks is more than 11 blocks?