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I U S A E The heights of adult men in America are normally distributed, with a mean of In the country of United States of Heightlandia, the height measurements of 69.3 inches and a standard deviation of 2.64 inches. The heights of adult ten-year-old children are approximately normally distributed with a mean of women in America are also normally distributed, but with a mean of 64.6 55.7 inches, and standard deviation of 8.3 inches. inches and a standard deviation of 2.58 inches. A) What is the probability that a randomly chosen child has a height of less a) if a man is 6 feet 3 inches tall, what is his z-score (to two decimal places)? than 65.05 inches? Z= Answer= (Round your answer to 3 decimal places.) b) if a woman is 5 feet 11 inches tall, what is her z-score (to two decimal B) What is the probability that a randomly chosen child has a height of more places)? than 61.4 inches? Answer= (Round your answer to 3 decimal places.) c) Who is relatively taller? A manufacturer knows that their items have a normally distributed lifespan, O The 5 foot 11 inch American woman with a mean of 9.5 years, and standard deviation of 2.7 years. O The 6 foot 3 inch American man If you randomly purchase one item, what is the probability it will last longer *** 1 foot = 12 inches *** than 4 years? The mean daily production of a herd of cows is assumed to be normally A study was conducted on students from a particular high school over the last 8 years. The following information was found regarding standardized test distributed with a mean of 40 liters, and standard deviation of 8.6 liters. used for college admitance. Scores on the SAT test are normally distributed with a mean of 1105 and a standard deviation of 202. Scores on the ACT test A) What is the probability that daily production is between 21.5 and 64.4 liters are normally distributed with a mean of 21.7 and a standard deviation of 4.9. It Do not round until you get your your final answer. is assumed that the two tests measure the same aptitude, but use different scales. Answer= (Round your answer to 4 decimal places.) If a student gets an SAT score that is the 76-percentile, find the actual SAT score. Warning: Do not use the Z Normal Tables...they may not be accurate enough SAT score = since WAMAP may look for more accuracy than comes from the table Round answer to a whole number. What would be the equivalent ACT score for this student? ACT score = Round answer to 1 decimal place. If a student gets an SAT score of 1570, find the equivalent ACT score. ACT score = Round answer to 1 decimal place. Question Help: Message instructor Engineers must consider the diameters of heads when designing helmets. The company researchers have determined that the population of potential clientele have head diameters that are normally distributed with a mean of 6.4 in and a standard deviation of 0.9-in. Due to financial constraints, the helmets will be designed to fit all men except those with head diameters that are in the smallest 4.1% or largest 4.1% What is the minimum head diameter that will fit the clientele? min = What is the maximum head diameter that will fit the clientele? max = Enter your answer as a number accurate to 1 decimal place. Answers obtained using exact z-scores or z-scores rounded to 3 decimal places are accepted Question Help: Message instructor