Could you please answer these two questions?

The Centers for Disease Control and Prevention reported that 20% of preschool children lack required immunizations.For a random sample of 64 children, approximate the probability that there are at most 9 children without immunizations. Let X = the number of sampledchildren without immunizations.

a)Though we could determine this probability using the exact binomial distribution, this would be time consuming to do by hand.Provide the justification that allows you to instead use the normal approximation to the binomial, making sure to include relevant formulas with correct notation and calculations.

b)Use the normal approximation to the binomial to determine the approximate probability that at most 9 of the sampled children will lack the required immunizations.Show all your work.Include (upload) an image that shows the area of the approximate probability using the normal approximation. (Note: as always, include your name and a title for your image.)

Google recently came in at number four on CNN Money's list of the 100 best companies to work for.Employees enjoy free gourmet lunches and snacks, freedom to bring pets to work and free fitness classes are among some of the employee perks at Google.As part of the application process, each candidate must pass an entrance exam.The candidate scores on the Google entrance exam follow a normal distribution with a mean of 60 points and a standard deviation of 12 points.If a candidate is a top performer, scores more than 75 points on the entrance exam, they are automatically asked for a phone interview.However, if a candidates scores in the top 30% of the distribution, the candidate is invited to take the entrance exam again within two weeks of the original exam date, otherwise the candidate must wait at least 1 year before attempting the exam again.

The standard deviation reported is 12 points.Consider each statement below and select all that are correct statements regarding an interpretation of or a use of this standard deviation.

• The average distance between the Google entrance exam scores is roughly 12 points.
• On average, the Google entrance exam scores vary from the mean score of 60 points by about 12 points.
• We would expect 99.7% of all Google entrance exam scores to be between 24 points and 96 points.
• The average Google entrance exam score is roughly 12 points from the mean Google entrance exam score of 60 points.

What is the minimum score that a candidate in the top 30% of the distribution can get in order to be invited to take the entrance exam again?

• 72 points
• 53.76 points
• 66.24 points
• 84 points

What proportion of candidates are automatically asked for a phone interview?

• 0.16
• 0.68
• 0.1056
• 0.8944
• 0.84