1) IQ is normally distributed with a mean of 100 and a standard deviation of 15.

Question

1) IQ is normally distributed with a mean of 100 and a standard deviation of 15. Suppose one individual is randomly chosen. Let X = IQ of an individual.

Find the probability that the person has an IQ greater than 125. What is the probability? (Round your answer to four decimal places.)

2) Suppose 4-year-olds in a certain country average 3 hours a day unsupervised and that most of the unsupervised children live in rural areas, considered safe. Suppose that the standard deviation is 1.8 hours and the amount of time spent alone is normally distributed. We randomly survey one 4-year-old living in a rural area. We are interested in the amount of time the child spends alone per day.

Find the probability that the child spends less than 1 hour per day unsupervised. What is the probability? (Round your answer to four decimal places.)

60% of the children spend at least how long per day unsupervised? (Round your answer to two decimal places.)

3)Terri Vogel, an amateur motorcycle racer, averages 129.71 seconds per 2.5 mile lap (in a 7 lap race) with a standard deviation of 2.28 seconds. The distribution of her race times is normally distributed. We are interested in one of her randomly selected laps.

Find the percent of her laps that are completed in less than 134 seconds. (Round your answer to two decimal places.)

Explanation / Answer

As per the Chegg policy, we are advised to do only one question at a time so i am attempting 1st.

1. Given,

Mean = 100

SD = 15

Hence,

P(IQ score > 125)

= P(X > 125)

= P(z > (125 - 100)/15)

= P(z > 1.67)

= 0.0478

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