Part 1) Amount of Sleep(7 points)

A sleep study administered to U.S. adults showed that the amount of sleep (in hours) they get in a 24-hour period is normally distributed with a mean of 6.5 hours and a standard deviation of 1.25 hours. Use normal probability calculations to answer the following questions.

Show your calculator functions to receive full credit. Round your answers to 4 decimals.

A. How many hours of sleep did you get last night (round to the nearest quarter of an hour)?

____________

B. Ask an adult friend or a family member how many hours of sleep he/she got last night (round to the nearest quarter of an hour). Report below. Make sure it is different than your sleep amount.

____________

1. (1 pt) What is the probability that a randomly selected U.S. adult slept less than your friend or family member did last night?

1. (1 pt) What is the probability that a randomly selected U.S. adult slept more than you did last night?

1. (1 pt) Doctors recommend 8 hours of sleep per day for adults to have the health benefits of sleep. What percent of U.S. adults sleep less than this recommended amount?

1. (1 pt) A colleague at work says that she usually sleeps less than 4 hours each day. Is her sleep amount unusual? Justify your answer by calculating its probability.

1. (1 pt) 10% of U.S. adults sleep more than how many hours?

1. (1 pt) A simple random sample of 25 U.S. adults is taken. What is the mean and standard deviation of the sampling distribution of sample means? Report your answers using the proper symbols.

1. (1 pt) A simple random sample of 25 U.S. adults is taken. What is the probability that the sample mean hours slept is less than what you slept last night?

Part 2) Effect of Covid Lockdowns on Speech and Language Skills(6 points)

A research study in England⁽¹⁾ done by The Education Endowment Foundation (EEF) suggests the measures taken to combat the pandemic have deprived the youngest children of social contact and experiences essential for increasing vocabulary. The study sampled 58 primary schools and found 76% of schools stated students starting school in 2020 needed more communication support than in previous school years.

Show calculator functions to answer the following questions.

1. (2 pt)Find the mean and standard deviation of the sampling distribution of the sample proportion of schools stating students starting school in 2020 needed more communication support than in previous years.

1. (2 pt)What is the probability that the sample proportion of schools stating students starting school in 2020 needed more communication support than in previous years is greater than 70%?

1. (2 pt)What is the probability that the sample proportion of schools stating students starting school in 2020 needed more communication support than in previous years is between 50% and 80%?