{"id":4639,"date":"2023-02-23T20:28:18","date_gmt":"2023-02-23T20:28:18","guid":{"rendered":"https:\/\/www.goodacademic.com\/blog\/questions\/calculate-probabilities-with-the-binomial-distribution\/"},"modified":"2023-02-23T20:28:18","modified_gmt":"2023-02-23T20:28:18","slug":"calculate-probabilities-with-the-binomial-distribution","status":"publish","type":"questions","link":"https:\/\/www.goodacademic.com\/blog\/questions\/calculate-probabilities-with-the-binomial-distribution\/","title":{"rendered":"Calculate probabilities with the binomial distribution"},"content":{"rendered":"<p><\/p>\n<p><em>Every day, 17% of the U.S. population with Internet access checks the weather in that way. For a sample of 5 people taken on any given day:<\/em><\/p>\n<ol>\n<li><em>Construct a table of the binomial probability distribution for this case.<\/em><\/li>\n<li><em>View this information using a histogram.<\/em><\/li>\n<li><em>Calculate the mean, variance, and standard deviation for this distribution.<\/em><\/li>\n<li><em>Calculate the probability that at least 3 people in the sample checked the weather that day.<\/em><\/li>\n<\/ol>\n<p><\/p>\n<p><em>According to a recent infographic (NAMI: National Alliance on Mental Illness, n.d.), &#8220;1 in 20 U.S. adults experience serious mental illness&#8221; in the United States. If a random sample of 20 students is selected from a large school district,&nbsp;<\/em><\/p>\n<ol>\n<li><em>Construct a table of the binomial probability distribution for this case.<\/em><\/li>\n<li><em>View this information using a histogram.<\/em><\/li>\n<li><em>Calculate the mean, variance, and standard deviation for this distribution.<\/em><\/li>\n<li><em>If 3 of the students were diagnosed with serious mental illness, would this be a signal about the school district having a problem with mental health among the students being above the national score?<\/em><\/li>\n<\/ol>\n","protected":false},"excerpt":{"rendered":"<p>Every day, 17% of the U.S. population with Internet access checks the weather in that way. For a sample of 5 people taken on any given day: Construct a table of the binomial probability distribution for this case. View this information using a histogram. Calculate the mean, variance, and standard deviation for this distribution. Calculate [&hellip;]<\/p>\n","protected":false},"author":3,"featured_media":0,"comment_status":"open","ping_status":"closed","template":"","meta":[],"disciplines":[533],"paper_types":[],"tagged":[],"aioseo_notices":[],"_links":{"self":[{"href":"https:\/\/www.goodacademic.com\/blog\/wp-json\/wp\/v2\/questions\/4639"}],"collection":[{"href":"https:\/\/www.goodacademic.com\/blog\/wp-json\/wp\/v2\/questions"}],"about":[{"href":"https:\/\/www.goodacademic.com\/blog\/wp-json\/wp\/v2\/types\/questions"}],"author":[{"embeddable":true,"href":"https:\/\/www.goodacademic.com\/blog\/wp-json\/wp\/v2\/users\/3"}],"replies":[{"embeddable":true,"href":"https:\/\/www.goodacademic.com\/blog\/wp-json\/wp\/v2\/comments?post=4639"}],"version-history":[{"count":0,"href":"https:\/\/www.goodacademic.com\/blog\/wp-json\/wp\/v2\/questions\/4639\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.goodacademic.com\/blog\/wp-json\/wp\/v2\/media?parent=4639"}],"wp:term":[{"taxonomy":"disciplines","embeddable":true,"href":"https:\/\/www.goodacademic.com\/blog\/wp-json\/wp\/v2\/disciplines?post=4639"},{"taxonomy":"paper_types","embeddable":true,"href":"https:\/\/www.goodacademic.com\/blog\/wp-json\/wp\/v2\/paper_types?post=4639"},{"taxonomy":"tagged","embeddable":true,"href":"https:\/\/www.goodacademic.com\/blog\/wp-json\/wp\/v2\/tagged?post=4639"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}