Question

Use the appropriate normal distribution to approximate the resulting binomial distribution A coin is weighted so that the probability of obtaining a head in a single tos:s is 0.6. If the coin is tossed 30 times, find the following probabilities. (Round your answers to four decimal places.) (a) fewer than 15 heads (b) between 15 and 19 heads, inclusive (c) more than 22 heads

Answer 1

Let x =number of heads

given n = 30 , p = 0.6 ,then q = 1 - p = 0.4

consider normal approximation .

then $\dpi{100} \fn_cm \mu$ = np = 30 x 0.6 = 18

and $\dpi{100} \fn_cm \sigma$ = $\dpi{100} \fn_cm \sqrt{npq}$ = $\dpi{100} \fn_cm \sqrt{30 \times 0.6\times 0.4}$ = 2.68

ie x ~ N ($\dpi{100} \fn_cm \mu$ , $\dpi{100} \fn_cm \sigma$ ) with $\dpi{100} \fn_cm \mu$ = 18 and   $\dpi{100} \fn_cm \sigma$ = 2.68

Then ,